Let A_1, B_1, C_1 be three points in the xy-plane. Suppose that the lines A_1C_1 and B_1C_1 are tangents to the curve y^2 = 8x at A_1 and B_1, respectively. If O = (0, 0) and C_1 = (-4, 0), then which of the following statements is (are) TRUE?

JEE Advanced 2024 Mathematics question

Let be three points in the -plane. Suppose that the lines and are tangents to the curve at and , respectively. If and , then which of the following statements is (are) TRUE?

(A)The length of the line segment is Correct
(B)The length of the line segment is 16
(C)The orthocenter of the triangle is Correct
(D)The orthocenter of the triangle is

Answer: (A),(C)

Solution

For () the tangent at is . It passes through when , i.e. . So and . – (A) TRUE. – (B) FALSE. The triangle is

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Question ID VK-034221