Ellipse

Question 1

Equation of ellipse when the focus and the directrix is given

Answer 1

(x-a)^2 + (y-b)^2 = e^2(lx+my+n/root (l^2+m^2))^2

Question 2

Alternate definition of ellipse

Answer 2

x^2/a^2 + y^2/b^2 = 1

Question 3

What is the range of x and y values?

Answer 3

x belongs to -a to a and y belongs to -b to b

Question 4

What is the ecentricity value?

Answer 4

e = root(1-b^2/a^2)

Question 5

Major Axis

Answer 5

Line passing through two focii

Question 6

Minor Axis

Answer 6

Line perpendicular to the major axis passing through the centre

Question 7

Vertices

Answer 7

Point of ellipse with the major axis

Question 8

Length of major and minor axis is

Answer 8

2a and 2b

Question 9

Ends of L.R. and length of L.R.

Answer 9

(±ae, ±b^2/a)
Length of L.R. = 2b^2/a

Question 10

Focal Distance

Answer 10

PS’ +PS = 2a(length of the major axis)

Question 11

Auxillary Circle of ellipse

Answer 11

Circle described on the major axis as the diameter
x^2+y^2 = a^2

Question 12

Parametric Coordinates of an ellipse

Answer 12

(acosθ, bsinθ)

Question 13

Tangent Conditions based on discriminant

Answer 13

D=0

Question 14

Conditions of tangency

Answer 14

c = ±root(a^2m^2 + b^2)

Question 15

Point Form equation of tangent

Answer 15

xx1/a^2 + yy1/b^2 = 1

Question 16

Parametric form equation of tangent

Answer 16

xcosθ/a + ysinθ/b = 1

Question 17

Slope form of tangent

Answer 17

y = mx±root(a^2m^2 + b^2)

Question 18

Tangents from an external point

Answer 18

m^2(h^2-a^2) - m(2hk) + k^2 - b^2=0

Question 19

Point form equation of normals to an ellipse

Answer 19

a^2x/x1 - b^2y/y1 = a^2-b^2

Question 20

Parametric form of normals to an ellipse

Answer 20

axsecθ-bycosecθ = a^2-b^2

Question 21

Slope form of normal of an ellipse

Answer 21

y = mx∓m(a^2-b^2)/root(a^2+b^2m^2)

Question 22

How many normals can pass through a point, and how many normals can be drawn from a point?

Answer 22

4,2