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. $\left( 1,\mspace{6mu}\frac{11}{4} \right)$
• B. $\left( 2,\mspace{6mu}\frac{11}{4} \right)$
• C. $\left( 3,\mspace{6mu}\frac{13}{4} \right)$
• D. $\left( 2,\mspace{6mu}\frac{13}{4} \right)$

Answer 1

Answer: (B)

$\left( 2,\mspace{6mu}\frac{11}{4} \right)$

Answer 2

AC is || to y axis it’s mid pt. is (2, 2)

Thus B(3, 2) & D(1, 2)

Equation of parabola

(x – 2)² = l(y – 3)

it is passes through (3, 2)

1 = – l Ž l = – 1

(x – 2)² = – (y – 3)

focus x – 2 = 0, y – 3 = –$\frac{1}{4}$ Ž $\left( 2,\frac{11}{4} \right)$