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Neetu 08/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Conic Sections

Find the equation of the circle whose centre is (3, 6) and which passes through the point (-1, 1)?

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Sarvajeet replied | 03/12/2016

Square of (x-3) + Square of (x-6) = 41.

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Neha 08/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Conic Sections

Find the whether (1, 3) lies inside, or outside or on the circle (square of x) + (square of y) = 16?

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Gunturi replied | 03/12/2016

Substitute those values in the L.H.S of the equation. if
LHS < RHS --- Lies Inside
LHS = RHS ---- Lies on the circle
LHS > RHS ---- Lies outside of the circle.

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Sarvajeet replied | 03/12/2016

Inside.

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R

Rakhi 08/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Conic Sections

Show that the point (5, 6) outside the circle: (square of x) + (square of y) = 4?

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Sarvajeet replied | 03/12/2016

S'=(square of 5) + (square of 6) - 4 = -57.

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Tapas replied | 04/12/2016

The equation of the circle is:
x^2 + y^2 = 4 = 2^2.
Therefore the radius of the circle is 2 units with its center at (0, 0). So, any point at a distance bigger than 2 units must be outside the circle.
Distance between the center (0, 0) and point (5, 6) is:
Sq. root of [(5-0)^2 + (6-0)^2] = sq root of (25 + 36) = sq root of 61 = 7.8. This is greater than the radius...  more»
The equation of the circle is:
x^2 + y^2 = 4 = 2^2.
Therefore the radius of the circle is 2 units with its center at (0, 0). So, any point at a distance bigger than 2 units must be outside the circle.
Distance between the center (0, 0) and point (5, 6) is:
Sq. root of [(5-0)^2 + (6-0)^2] = sq root of (25 + 36) = sq root of 61 = 7.8. This is greater than the radius of the circle. So the point (5, 6) is outside the circle. «less

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Raj 08/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Conic Sections

Find the equation of the circle which passes through the points (1, 2), (2, 2) and (4, -1)?

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Sarvajeet replied | 03/12/2016

square of (x-3/2) + square of (y-3/2) = 1/2.

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Tapas replied | 04/12/2016

Take the general equation for a circle:
x^2 + y^2 + 2gx + 2fy + c = 0, where the center is at (-g, -f) and the radius is sq root of (g^2 +f^2 -c).
Now use the given points to get three equations to solve for three unknowns, g, f, and c. The equations with point (1, 2) becomes:
1^2 + 2^2 + 2xgx1 + 2xfx2 + c = 0
=> 2g + 4f + c = - 5 .............. (1)
Similarly,...  more»
Take the general equation for a circle:
x^2 + y^2 + 2gx + 2fy + c = 0, where the center is at (-g, -f) and the radius is sq root of (g^2 +f^2 -c).
Now use the given points to get three equations to solve for three unknowns, g, f, and c. The equations with point (1, 2) becomes:
1^2 + 2^2 + 2xgx1 + 2xfx2 + c = 0
=> 2g + 4f + c = - 5 .............. (1)
Similarly, the equation with the point (2, 2) is:
=> 4g + 4f + c = - 8 .............. (2)
And, the equation with the point (4, -1) is:
=> 8g - 2f + c = - 17 .............. (3)

From (1) - (2) we get: -2g = 3 --> g = -3/2.
Using this value of g in (1) we get:
4f + c = - 2 ............ (4)
Using this value of g in (3) we get:
-2f + c = - 5 ............ (5)
From (4) - (5) we can get:
6f = 3 --> f = 1/2.
Using this value of f in (5) we get: c = - 4.
So, the equation of the circle is:
x^2 + y^2 + 2(-3/2)x + 2(1/2)y + (- 4) = 0.
After simplification:
--> x^2 + y^2 -3x +y - 4 = 0 (Answer) «less

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Harsh 08/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Conic Sections

Define latus rectum of a Parabola?

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Sarvajeet replied | 03/12/2016

The latus rectum of a parabola, square of y =4ax is 4a.

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Himanshu 08/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Conic Sections

Find the axis of the parabola: (square of y) = x?

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Sarvajeet replied | 03/12/2016

The x axis i.e., y = 0.

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S

Sammeyka 08/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Conic Sections

Find the equation of the line which passes through the focus of the Parabola: (square of y) = 20x?

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Sarvajeet replied | 03/12/2016

There are infinite number of lines at different slopes (including its axis) which pass through the focus (5,0) of the parabola, (square of y) = 20x. So, you tell me either one slope or one point.

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H

Himanshu 08/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Limits and Derivatives

What are the properties of limit?

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Rahulkumar replied | 26/11/2016

Limit stand for value of function. Near that value of variable not exactly at value of variable but very close to it.
It simply show how function behave at any value and we generally check it for extreme condition where we have doubt regarding behaviour of function and we can use other operator on them like differentiation and integration etc.

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A

Ananya 08/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Limits and Derivatives

What is the derivative of sin(x)?

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Puneet replied | 22/11/2016

-sin(x)

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Puneet replied | 22/11/2016

cos(x)

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R

Raveena 08/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Limits and Derivatives

What is the derivative of cos(x)?

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Tapas replied | 28/11/2016

- sin(x)

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S

Sakthivel 08/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Linear Programming

Define linear programming?

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Sreedevi replied | 07/12/2016

Linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.

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M

Medha 08/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Linear Programming

Define linear programming?

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Hussam Uddin replied | 22/11/2016

Set of values of points x, y which follows certain constraints.

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K

Kalyani 08/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Linear Programming

Define constraints with respect to linear programming?

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Hussam Uddin replied | 22/11/2016

Constraints is nothing but set of conditions which equations follow.

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B

Bijoy 09/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Mathematical Reasoning

Change the statement to negative statement: p - New Delhi is a city?

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Manan replied | 19/11/2016

New Delhi is not a village.

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T

Tushar 09/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Mathematical Reasoning

Write the negation of the given statement: root 7 is a rational number?

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Prateek replied | 19/11/2016

No, irrational.

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A

Ankush 09/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Mathematical Reasoning

What do you mean by compound statement with respect to mathematical reasoning?

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Sreedevi replied | 07/12/2016

When two simple statements are joined by using connectives like ^,V, implication,bi implication and negation a compound statement is formed.

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S

Sushma 09/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Mathematical Reasoning

Fill up a statement which having a relation: Window is to pane as book is to____?

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Shreyans replied | 08/12/2016

Cover.

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P

Pankaj 09/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Mathematical Reasoning

What number should come next in the given series: 2, 1, (1 / 2), (1 / 4), …. ?

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Tapas replied | 28/11/2016

1/8

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Chandan replied | 30/11/2016

1/8 as it is decreasing GP.

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Preeti 09/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Matrices

What do you mean by order of matrix?

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Chilla Rajesh replied | 02/12/2016

The no. of rows and columns in matrix.

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Brunda 09/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Matrices

What is the general equation of matrix?

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S

Shiv replied | 19/11/2016

AX=B

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S

Sujatha 09/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Matrices

Construct a 3 x 2 matrix whose elements are given by: a(ij) = 1 / 2[i - 3j]?

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Richa replied | 19/11/2016

The answer is given below

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Sanket 09/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Matrices

Define column matrix and row matrix?

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Shreyans replied | 08/12/2016

Column matrix : 1 or more than 1 row and only 1 column matrix called column matrix [mX1].
Row matrix : 1 or more than 1 column and only 1 row matrix called row matrix [1Xn] . e.g [1 5 3] it's 3*1.

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A

Ashmita 09/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Matrices

Define square matrix?

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Chilla Rajesh replied | 01/12/2016

A matrix consist of m rows and n column, where m = n.

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Rasneet 09/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Matrices

What do you mean by equality of matrix?

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Tapas replied | 27/11/2016

If each matrix has:-
(1) the same number of rows,
(2) the same number of columns and
(3) corresponding elements within each matrix are equal then the two matrices are said to be equal.

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Neeta 09/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Matrices

Given: A = [3 8 9] and B = [-2 3 0]; find A + B?

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Sarvajeet replied | 23/11/2016

[1 11 9].

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