Let E denote the parabola y^2=8x. Let P=-2,4, and let Q and Q^(') be two distinct points on E such that the lines PQ and PQ^(') are tangents to E. Let…

Question

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

MARKS Content Team · Accepted Answer

Correct answer: (A) The triangle PFQ is a right-angled triangle; (B) The triangle QPQ^(') is a right-angled triangle; (D) F lies on the line joining Q and Q^('). y^2=8x ⇒a=2, Focus F2,0, and Directrix x=−2 ∵ P−2,4 lies on directrix ⇒ QQ^(') will be a focal chord and tangents are mutually perpendicular. ⇒ ΔQPQ^(') is right angled. Also the portion between point of contact and directrix of parabola subtends right angle at the focus. So, △PFQ is a right- angled triangle. PF=√(−2−2^2+4−0^2)=4√2

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

Solution

More Parabola Questions

Let E denote the parabola y2=8x. Let P=-2,4, and let Q and Q' be two distinct points on E such that the lines PQ and PQ' are tangents to E. Let F be the focus of E. Then which of the following statements is (are) TRUE?

Solution

More Parabola Questions

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