Ellipse Flashcards

1
Q

What is the standard equation of an ellipse?

A

x^/a^ + y^/b^= 1

Where b^=a^(1-e^)

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2
Q

How do you prepare the equation of an ellipse?

A

If s is the focus , e is the eccentricity, and P is any point on the ellipse , then

SP/PM =e

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3
Q

What is latus rectum ?

A

Latus rectum is a double ordinate passing through the focus.

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4
Q

What is focal distance ?

A

Focal distance is the distance of any point on the ellipse from its foci.

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5
Q

For a>b , what are the coordinate of verties of ellipse ?

A

(a,0) and (-a,0)

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6
Q

For a>b , what are the coordinate of foci of ellipse ?

A

(ae,0) and (-ae,0)

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7
Q

For a>b , what are the lengths of major axis and minor axis ?

A

Length of major axis is 2a (eq y=0)and length of minor axis is 2b(eq x=0)

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8
Q

For a>b , what is the equation of directrices ?

A

x= a/e and x=-a/e

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9
Q

For a>b , what is the eccentricity of ellipse ?

A

e= [1-b^/a^]^1/2

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10
Q

For a>b , what is the length of latus rectum ?

A

2b^/a

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11
Q

For a>b , what is the focal distance of point (x,y)

A

a+ex and a-ex

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12
Q

For b>a, what is the length of major axis and minor axis ?

A

Length of major axis is 2b and length of minor axis is 2a

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13
Q

For b>a, what is the length of latus rectum ?

A

Length of latus rectum is 2a^/b

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14
Q

The sum of focal distances of any two points on an ellipse is equal to what?

A

Major axis.

S’P+SP=2a

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15
Q

What is an auxiliary circle ?

A

Circle described on the major axis as diameter is called auxiliary circle.
x^+y^=a^.
x= a cos # and y= b sin # satisfied the equation of the ellipse.

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16
Q

What is the parametric equation of an ellipse ?

A

x=a cos # and y= b sin # is the parametric equation of ellipse x^/a^ + y^/b^ = 1.

17
Q

What is the equation of the tangent to a point (x1,y1) of an ellipse ?

A

xx1/a^ + yy1/b^ = 1

18
Q

What is the equation of tangent to an ellipse in parametric form ?

A

(x cos #)/a + (y cos #)/b=1

19
Q

Why is the equation of tangent to an ellipse in slope form ?

A

If c = +- [a^m^+b^]^1/2 then equation of tangent to the ellipse is y = mx +- [a^m^+b^]^1/2

20
Q

In an ellipse , foot of perpendicular from any focus to any tangent always lies on what?

A

Auxiliary circle.

21
Q

What angle does the portion of tangent to parabola or ellipse or hyperbola between the point of contact and the directrix substends ?

A

90( right angle)