Question

In the adjacent figure a parabola is drawn to pass through the vertices B, C and D of the square ABCD. If A(2, 1), C(2, 3) then focus of this parabola is -

(a)  (1, 11/4)

(b)  (2, 11/4)

(c)  (3, 13/4)

(d)  (2, 13/4)

Answer 1

Correct option (c)  (2, 11/4)

Explanation:

Clearly AC is parallel to y-axis. It’s midpoint is (2, 2).

Thus B= (1, 2). Parabola will be in the form of (x – 2)² = λ(y – 3).

It passes through (3,2)

⇒ l = -λ. Thus parabola is (x – 2)² = – 1(y – 3).

It focus is x - 2 = 0.

y - 3 = -1/4, i.e., (2,11/4)