Question

L3If the focal distance of an end of the minor axis of any ellipse (its axes as x and y axis respectively) is k and the distance between the foci is 2h, then its equation is-

• A. $\frac{x^{2}}{k^{2}} + \frac{y^{2}}{h^{2}}$ = 1
• B. $\frac{x^{2}}{k^{2}} + \frac{y^{2}}{k^{2}–h^{2}}$ = 1
• C. $\frac{x^{2}}{k^{2}}–\frac{y^{2}}{k^{2}–h^{2}}$ = 1
• D. $\frac{x^{2}}{k^{2}} + \frac{y^{2}}{k^{2} + h^{2}}$ = 1

Answer 1

Answer: (B)

$\frac{x^{2}}{k^{2}} + \frac{y^{2}}{k^{2}–h^{2}}$ = 1

Answer 2

Let equation of ellipse is $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}$ = 1 and e is eccentricity of ellipse.

Therefore 2h = 2ae

ae = h. ....(1)

Focal distance of one end of minor axis say

(0, b) is k,

Therefore a + e (0) = k

a = k ....(2)

Therefore by (1) and (2)

b2 = a2 (1 – e2)

b2 = a2 – a2e2 = k2 – h2

Therefore equation of ellipse $\frac{x^{2}}{k^{2}} + \frac{y^{2}}{k^{2}–h^{2}}$ = 1.