Question

Let y² = 4ax be parabola and PQ be a focal chord of parabola. Let T be the point of intersection of tangents at P and Q. Then

• A. Area of circumcircle of DPQT is $\left( \frac{\pi(PQ)^{2}}{4} \right)$
• B. Orthocenter of DPQT will lie on tangent at vertex.
• C. Incenter of DPQT will be vertex of parabola.
• D. Incentre of DPQT will lie on directrix of parabola.

Answer 1

Answer: (A)

Area of circumcircle of DPQT is $\left( \frac{\pi(PQ)^{2}}{4} \right)$

Answer 2

for focal chord t₁t₂ = – 1

Tangent drawn at the extremities of focal chord are perpendicular and meet at directrix

ĐPTQ = 90⁰

Hence PQ is diameter of circum circle of DPTQ.

2r = PQ ̃ r = (PQ/2)

Area of circum circle pr² = $\frac{\pi(PQ)^{2}}{4}$