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 ?

JEE Advanced 2021 Mathematics question

Let denote the parabola . Let , and let and be two distinct points on such that the lines and are tangents to . Let be the focus of . Then which of the following statements is (are) TRUE ?

(A)The triangle is a right-angled triangleCorrect
(B)The triangle is a right-angled triangleCorrect
(C)The distance between and is
(D) lies on the line joining and Correct

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

Solution

: , focus , directrix ; lies on the directrix. Tangent at : ; through : , . (B) Slopes of the tangents are with product , so $ QPQ' =

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Question ID VK-033940