Question

Let A1, B1, C1 be three points in the xy -plane. Suppose that the lines A1C1 and B1C1 are tangents to the curve y2 = 8x at A1 and B1, respectively. If O = (0,0) and C1 = −( 4, 0), then which of the following statements is (are) TRUE ?

• A. The length of the line segment OA1 is $4\sqrt3$
• B. The length of the line segment A1B1 is 16
• C. The orthocenter of the triangle A1B1C1 is (0, 0)
• D. The orthocenter of the triangle A1B1C1 is (1, 0)

Answer 1

Answer: (A), (C)

The length of the line segment OA1 is $4\sqrt3$

Answer 2

The correct option is (A): The length of the line segment OA1 is $4\sqrt3$ and (C): The orthocenter of the triangle A1B1C1 is (0, 0).