Extremities of the latera recta of the ellipses `(x^2)/(a^2)+(y^2)/(b^2)=1(a > b)` having a given major axis 2a lies on

Options

A. `x^(2) = a(a-y)`
B. `x^(2) =a(a+y)`
C. `y^(2) =a(a+x)`
D. `y^(2) =a(a-x)`

Answer

A, B

Explanation

Let (h,k) be the extremity of L.R.
`:. h = +- ae, k = +- (b^(2))/(a)`
`:. k= +-a (1-e^(2)) = +-a (1-(h^(2))/(a^(2))) = +- (a-(h^(2))/(a))`
On taking + ve sign, we get
`k = a- (h^(2))/(a)`
`rArr (h^(2))/(a) = a -k rArr a-k rArr h^(2) =a (a-k)`.
On taking -ve sign, we get
`k =- a+(h^(2))/(a)`
`rArr h^(2) = a(a+k)`