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Lesson Posted on 17/08/2018 Learn Co-ordinate Geometry
Raj Kumar
I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...
Ellipse is a regular oval shape, traced by a point moving in a plane so that the
the sum of its distances from two other points (the foci) is constant
When a cone is cut by an oblique plane which does not intersect the base, it results in the formation of an ellipse.
Standard equation of the ellipse is given as
x2/a2+y2/b2=1
and eccentricity of the ellipse lies between 0 and 1
the eccentricity of an ellipse is given as
e=√1-b2/a2 when a>b
Foci of an ellipse are (±ae,0)
Major Axis=2a
Minor Axis=2b
The equation of Directrix are x=±a/e
Coordinates of vertices are (±a,0)
Length of latus rectum is 2b2/a.
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Lesson Posted on 17/08/2018 Learn Co-ordinate Geometry
Tangent and normal ,Subtangent,Subnormal
Raj Kumar
I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...
Equation of tangent at P(x,y) to the curve y=f(x) is given as
Y-y=dy/dx(X-x)
Equation of Normal at P(x,y) to the curve y=f(x) is given as
Y-y=-1/dy/dx(X-x)
By applying the condition of perpendicularity
If product of slopes of lines will be equal to -1 lines are perpendicular
as we know that normal and tangent will be perpendicular to each other
m1m2=-1
let slope of tangent is m1=dy/dx
so solpe of normal will be m2=-1/m1=-1/dy/dx
length of tangnet will be y=√1+(dx/dy)2
Length of normal will be y=√1+(dy/dx)2
length of Sub-Tangent will be ydx/dy
length of Sub-normal will be ydy/dx
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Lesson Posted on 03/01/2018 Learn Co-ordinate Geometry
Raj Kumar
I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...
Graphical Transformation:
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Lesson Posted on 03/01/2018 Learn Co-ordinate Geometry
Gradient (Slope) Of Line / Inclination
Raj Kumar
I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...
tan α = opposite/adjacent
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Lesson Posted on 27/12/2017 Learn Co-ordinate Geometry
Raj Kumar
I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...
Transformation is basically the "change of form"
Etymology Trans = across, bayond + formare = to form
These transformations fall into two categories:
i. Rigid transformations that do not change the shape or size of the pre-image
ii. Non-rigid transformations that change the size but not the shape of the pre-image.
Basically four type of transformation:
1) Translation (Shifting/Sliding in linear direction) or Horizontal or vertical movement either upward or downward
2) Rotation:
i. A rotation is atransformation in which the object is rotated about a fixed point.
ii. Turn Around either in Clockwise or in anticlockwise/Counterclockwise direction
Reflection can be:
a. Around X axis
b. Around Y Axis
c. Around line Y=X or Y=-X
d. Around the Origin
3) Reflection:
i. Mirror Image of anything
ii. It is basically a 'flip' of a shape over the line of reflection
4) Dilation:
i. Dilation that creates a smaller image is called a reduction.
ii. A dilation stretches or shrinks the original figure.
iii. A description of a dilation includes the scale factor (or ratio) and the center of the dilation.
read lessLesson Posted on 27/12/2017 Learn Co-ordinate Geometry
Raj Kumar
I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...
Important Properties of Paralleolgram:
1) Opposite side length are Exactly Equal or Congruent that means.
2) Both line pairs will be parallel to each other.
3) Opposite parallel lines slopes are equal.
4) Area of paralellogram = Base X Altitude.
5) Opposite angles are exactly equal or congruent.
6) Sum of adjacent or consective angles is 180°.
7) If one angle is 90° then all angles will be 90°.
8) Diagnols of parallelogram bisect each other.
9) Each diagonal of parallelogram seperates into two exactly equal triangles.
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Answered on 14/12/2016 Learn Co-ordinate Geometry
Ravikumar
Answered on 14/12/2016 Learn Co-ordinate Geometry
Ravikumar
Answered on 14/12/2016 Learn Co-ordinate Geometry
Ravikumar
Take Tuition from the Best Tutors
Answered on 14/12/2016 Learn Co-ordinate Geometry
Ravikumar
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