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# Ask a Mathematics(Class XI-XII Tuition (PUC)) Question

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N

Neha 14/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Find the locus of the extremities of the latus recta of all ellipses having a given major axis 6a?

Saurabh replied | 01/12/2016

Let LSI be the latus rectum, C be the centre of the ellipse and the coordinates of L be (x, y) then x = CS = 3 ae ...... (1)
And y = SL = b2/3a = (9a2(1 - e2))/3a = 3a (1 - e2) ...... (2)
Eliminating the variable 'e' from (1) and (2) we get the locus of L.
Hence putting the value of e from (1) and (2), we get:-
y = 3a(1-x2/9a2)
x2 = 9a2 - 3ay
x2 = 3a(3a -...  more»
Let LSI be the latus rectum, C be the centre of the ellipse and the coordinates of L be (x, y) then x = CS = 3 ae ...... (1)
And y = SL = b2/3a = (9a2(1 - e2))/3a = 3a (1 - e2) ...... (2)
Eliminating the variable 'e' from (1) and (2) we get the locus of L.
Hence putting the value of e from (1) and (2), we get:-
y = 3a(1-x2/9a2)
x2 = 9a2 - 3ay
x2 = 3a(3a - y), which is clearly a parabola. Similarly, we can show that the locus of L' is x2 = 3ay(y + 3a) which is again a parabola. «less

Tejas replied | 02/12/2016

Co-ordinate of extreme point of latus rectum would b (c,y).You can find ‘y’ by taking ‘x’ as ‘c’ in general equation,which comes out to b2/a.So the co-ordinate becomes {(a2-b2)1/2,b2/a}.Eliminating ‘b’ you will get a2-x2=ay.

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R

Rajini Sucharita 14/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

What is the equation of chord joining two points on the hyperbola?

Sudeesh replied | 26/11/2016

xy1 + yx1 = 2c * c.

Ankit replied | 09/12/2016

xy1 + yx1 = 2c * c.

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R

Raghbendra 14/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

What are the equation for finding the coordinates of the point of contact?

Rachna replied | 21/11/2016

To find the coordinates of point of contact you have to solve the equations simultaneously either by elimination method, or substitution or cross amulet up location method

Ankit replied | 09/12/2016

To find the coordinates of point of contact you have to solve the equations simultaneously either by elimination method, or substitution or cross amulet up location method.

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S

Sangeetha 14/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

What is the difference between the diameter and conjugate diameter?

Nirmal replied | 03/12/2016

Hello Sangeetha,
Two diameters are conjugate if each bisects the chords parallel to the other diameter. If you consider the Hyperbola and Parabola, things get a little complicated. It is much simpler in Circles and Ellipses. Consider reading this link if you want to know more.

http:/...  more»
Hello Sangeetha,
Two diameters are conjugate if each bisects the chords parallel to the other diameter. If you consider the Hyperbola and Parabola, things get a little complicated. It is much simpler in Circles and Ellipses. Consider reading this link if you want to know more.

Regards

Nirmal «less

Rahul replied | 05/12/2016

Hello Sangeetha,
If we talk about ellipse, any chord that passes through the center of an ellipse is call its diameter. It follows that the family of parallel chords define two diameters: one in the direction to which they are all parallel and the other the locus of their midpoints. Such two diameters are called conjugate.

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S

Sita 14/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Prove that the midpoints of chords of the hyperbola (square of x)/(square of a)–(square of y)/(square of b) = 1 parallel to the diameter y = mx lie on the diameter (square of a)my = (square of b) x?

Ankit replied | 09/12/2016

Answer to this question cant be texted. Have a live session with me.

A

Aravind replied | 12/12/2016

Let the cord parallel to y=mx be
y=mx+c..............(1)
Then the points of intersection with the hyperbola are given by:-

x^2/a^2 - (mx+c)^2/b^2 = 1
or (1/a^2-m^2/b^2)x^2-2mxc/b^2-c^2/b^2-1=0 .....(2)

Let (x1,y1) and (x2,y2) be the end points of the cord.
Then x1 and x2 both satisfy Eq.(2)

So x1+x2 = [2mc/b^2]/(1/a^2-m^2/b^2)
...  more»
Let the cord parallel to y=mx be
y=mx+c..............(1)
Then the points of intersection with the hyperbola are given by:-

x^2/a^2 - (mx+c)^2/b^2 = 1
or (1/a^2-m^2/b^2)x^2-2mxc/b^2-c^2/b^2-1=0 .....(2)

Let (x1,y1) and (x2,y2) be the end points of the cord.
Then x1 and x2 both satisfy Eq.(2)

So x1+x2 = [2mc/b^2]/(1/a^2-m^2/b^2)
= 2mc/(b^2/a^2-m^2)...............(3)

Let (h,k) be the midpoint of the cord. Then
h=(x1+x2)/2 = mc/(b^2/a^2-m^2)
and k=(y1+y2)/2.

Now both (x1,y1) and (x2,y2) satisfy Eq(1) so that
k=mh+c. Substituting the value of c from Eq(3)
k=mh+(b^2/a^2-m^2)h/m = b^2/(a^2m)
Or a^2 mk = b^2h
Therefore the locus of the midpoint (h,k) of the cord
is a^2 my = b^2x. «less

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P

Poonam 14/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Prove that the angle subtended by any chord of a rectangular hyperbola at the centre is the supplement of the angle between the tangents at the end of the chord?

Ankit replied | 09/12/2016

Solve with the help of parametric equations of hyperbola.

Mohit replied | 14/12/2016

Solve with the help of parametric equations of hyperbola.

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B

Bhupen 14/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

On a level plain the crack of the rifle and the thud of the ball striking the target are heard at the same instant, prove that the locus of the hearer is a hyperbola?

Jaya Laxmi Kl replied | 24/11/2016

Please find the solution screenshot.

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F

Furqankhan 14/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Find the locus of intersection of tangent to a hyperbola, which meet at a constant angle x?

R

Rita replied | 22/11/2016

Equation of hyperbola is x2/a2-y2/b2 = 1

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S

Soumya 14/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Find the equation to the hyperbola whose asymptotes are the straight lines x + 3y – 1= 0 and 2x – y + 7 = 0, and which passes through the point (1, 2)?

Chirag replied | 23/11/2016

Asymptotes are nothing but tangents at infinity take equation of tangents and solve it.

Chirag replied | 23/11/2016

Let equation of the hyperbola is (x-h)^2/a^2+(y-b)^2/b^2 and its asymptotes are given by:- y=+or-(b/a)(x-h)+k.
You can compare your equations with this and find relevant values of a, b, h, k and substitute in equation of hyperbola.

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D

Deepa 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

P

Prabha replied | 11/12/2016

8!-3!=8×7×6×5×4×3!- 3!= 3!(8×7×6×5×4-1)
=6(6720-1)=6×6719=40314.

K

K.vaishali replied | 11/12/2016

4x5x6x7x8=6720.

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M

Mahesh K 12/11/2016 in  Mathematics(Class XI-XII Tuition (PUC))

How can I learn integral calculus

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A

Aparna 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Daljit Kaur replied | 24/11/2016

64.

Hassan replied | 05/12/2016

1/6! +1/(7x6!) =1/(8x7x6!). Take LCM and solve will get x=64.

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N

Neelima 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Debojyoti Roy replied | 28/11/2016

118.

Sarvajeet replied | 06/12/2016

118.

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K

Kasireddy 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Determine order and degree of differential equation: dy/dx + 5y = 0?

0 0 4

Manish replied | 11/12/2016

1,1.

K

K.vaishali replied | 11/12/2016

Order=1, Degree=1.

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M

Mrs 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Solve with respect to x: y = e (power x) + 1?

0 0 4

S

Shiv replied | 19/11/2016

dy/dx=e(power)x

Hussam Uddin replied | 22/11/2016

y = 2+ x+ x2/2! + x3/3! + ....

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A

Arun 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Differentiate with respect to x: xy = log y + C?

0 0 4

Daljit Kaur replied | 24/11/2016

y+xy'= y'/y.

Tapas replied | 28/11/2016

x(derivative of y) + y(derivative of x) = derivative of (log y) + derivative of C.
remember C is a constant. So,
xy' + y=y'/y + 0 --> xy' + y = y'/y.

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A

Ankit 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

What do you mean by order and degree of the derivative?

0 0 3

Karuna replied | 22/11/2016

By order we mean number of times the variable has been differentiated and by degree we mean the maximum power of the highest order deriative.

Saddam replied | 24/11/2016

The order of a differential equation is the order of the highest order derivative present in the equation.
The degree of a differential equation is the power of the highest order derivative in the equation after it has been made rational and integral as far as derivatives are concerned.
dx is of order 2 and degree 3.

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A

Akhil 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Solve with respect to x: dy / dx = (1 - cos x) / (1 + cos x)?

0 0 3

Prateek replied | 19/11/2016

Rationalize it and then separate.

Sarvajeet replied | 02/12/2016

y= -x+2tan(x/2)+C.

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N

Nalini 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Define differentiability?

0 0 3

Hussam Uddin replied | 22/11/2016

Differential means derivative has a unique value at that point. If a curve is smooth it has only one differential value and it is called differential.

Sarvajeet replied | 07/12/2016

df/dx= lim f(x+h)-f(x)/ h at h->0.

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B

Bhuvana 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Evaluate: 8! / 6! * 2!?

0 0 4

Tapas replied | 01/12/2016

The problem should be mentioned more clearly. Is it (8!/6!)*2! or 8!/(!6*!2)?
If it is (8!/6!)*2! Then the solution:
8! = 8x7x6x5x4x3x2x1, 6! = 6x5x4x3x2x1, 2!=2. So, (8!/6!)*2! = 56x2 = 112.

If it is 8!/(6!*2!) The the solution:
8! = 8x7x6x5x4x3x2x1, 6! = 6x5x4x3x2x1, 2!=2. So, 8!/(6!*2!) = 56/2 = 28

Sreedevi replied | 01/12/2016

The problem is not clear. If we consider the problem as (8!/6!) * 2! we can proceed like this:
8! can be written as 8*7*6!. 6! can be cancelled both in the numerator and denominator. We are left with 8*7*2 ( since 2! = 2*1 =2) = 112.
If we consider the problem as 8!/(6!*2!). we get 28.

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R

Rahul 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

0 0 3

Y

Yash replied | 22/11/2016

8

Sarvajeet replied | 06/12/2016

8.

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M

Madhu 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

How many 5 - digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

0 0 3

Y

Yash replied | 22/11/2016

Rs. 336

Sarvajeet replied | 06/12/2016

336.

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D

Divya 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

How many 3 - digit numbers can be formed from the digits 1, 2, 3, 4, 6 assuming that repetition is not allowed?

0 0 4

Sarvajeet replied | 02/12/2016

60

Sanjeev replied | 03/12/2016

5C3*3! = 10*6 = 60.

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A

Ananya 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Define permutation?

0 0 3

Abhilash replied | 02/12/2016

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.

Sarvajeet replied | 06/12/2016

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permutation.

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P

Parminder 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

How many 3- digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?

0 0 4

Siva replied | 07/12/2016

336.

K

Kavya replied | 08/12/2016

504.

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