Question

Consider the parabola with its vertex at origin and the axis along the x-axis. The line y = 2x + c, where c > 0, is a common tangent to the parabola and the circle x² + y² = 5. Then then the

(A)  directrix is x = -10

(B)   focus is (10, 0)

(C)   latus rectum is 20

(D)   directrix is x = 10

Answer 1

Correct option  (A), (B)

Explanation 

 The line y = 2x + c touches the circle. This implies

c² = 5(1 + 2²) = 25

⇒ c = 5 (∴  c> 0)

Let y² = 4ax be the parabola. Since the line y = 2x + 5 touches the parabola we have

5 = a/2  or  a = 10

Therefore, the parabola is y²  =  40x. Hence, the focus is (10, 0).