Question

The number of values of c such that the line y = 4x + c  touches the ellipse x²/4 + y²/1 = 1 is

 (A)  0

(B)  1 

(C)  2

(D)  infinite

Answer 1

Correct option (c)  2

Explanation :

We have

⇒ c² = a²m² + b²

⇒ c² = 4(16) + 1 = 65

⇒ c² = ±√65

Hence, there are two values of c, namely, +√65 and - √65