Ellipse

Question 1

What is the standard equation of an ellipse?

Answer 1

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

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

Question 2

How do you prepare the equation of an ellipse?

Answer 2

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

SP/PM =e

Question 3

What is latus rectum ?

Answer 3

Latus rectum is a double ordinate passing through the focus.

Question 4

What is focal distance ?

Answer 4

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

Question 5

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

Answer 5

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

Question 6

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

Answer 6

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

Question 7

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

Answer 7

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

Question 8

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

Answer 8

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

Question 9

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

Answer 9

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

Question 10

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

Answer 10

2b^/a

Question 11

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

Answer 11

a+ex and a-ex

Question 12

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

Answer 12

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

Question 13

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

Answer 13

Length of latus rectum is 2a^/b

Question 14

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

Answer 14

Major axis.

S’P+SP=2a

Question 15

What is an auxiliary circle ?

Answer 15

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.

Question 16

What is the parametric equation of an ellipse ?

Answer 16

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

Question 17

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

Answer 17

xx1/a^ + yy1/b^ = 1

Question 18

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

Answer 18

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

Question 19

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

Answer 19

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

Question 20

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

Answer 20

Auxiliary circle.

Question 21

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

Answer 21

90( right angle)