Question

Let $E$ denote the parabola $y ^{2}=8 x$ Let $P =(-2,4)$ and let $Q$ and $Q ^{\prime}$ be two distinct points on $E$ such that the lines $P Q$ and $P Q^{\prime}$ are tangents to $E$ Let $F$ be the focus of $E$. Then which of the following statements is(are) TRUE?

• A. The triangle $PFQ$ is a right-angled triangle
• B. The triangle $QPQ '$ is a right-angle triangle
• C. The distance between $P$ and $F$ is $5 \sqrt{2}$
• D. $F$ lies on the line joining $Q$ and $Q'$

Answer 1

Answer: (A), (B), (D)

The triangle $PFQ$ is a right-angled triangle

Answer 2

(A) The triangle $PFQ$ is a right-angled triangle
(B) The triangle $QPQ '$ is a right-angle triangle
(D)$F$ lies on the line joining $Q$ and $Q'$