Question

Equation of the line passing through centre and bisecting the chord 7x + y = 20 of the ellipse x2 + y2/7 = 1, is

(A) x + y = 5

(B) x + y = 0

(C) x – y = 0

(D) x – y = 5

Answer 1

Correct Answer is: (C) x – y = 0

Let the mid-point of chord by (α, β), so its equation is αx + βy/7 = α2 + β2/7.

Now, on comparing with 7x + y = 20, we get α/7 = (β/7)/1 ⇒ α = β.

So, the required line be y = βx/α ⇒ y = x.