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Parabola question

2024 · Shift 2 · Q24

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PYQ Library
JEE Advanced
Mathematics
Parabola
2024 · Shift 2 · Q24

Parabola question

2024 · Shift 2 · Q24

JEE AdvancedMathematicsParabolaMultiple correct+4 / −2

Let

A_1, B_1, C_1

be three points in the

x y

-plane. Suppose that the lines

A_1 C_1

and

B_1 C_1

are tangents to the curve

y^2=8 x

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?

A
The length of the line segment $O A_1$ is $4 \sqrt{3}$
B
The length of the line segment $A_1 B_1$ is 16
C
The orthocenter of the triangle $A_1 B_1 C_1$ is $(0,0)$
D
The orthocenter of the triangle $A_1 B_1 C_1$ is $(1,0)$

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