1
JEE Advanced 2024 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Change Language
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 $(1,0)$
2
JEE Advanced 2022 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2
Change Language

Consider the parabola $$y^{2}=4 x$$. Let $$S$$ be the focus of the parabola. A pair of tangents drawn to the parabola from the point $$P=(-2,1)$$ meet the parabola at $$P_{1}$$ and $$P_{2}$$. Let $$Q_{1}$$ and $$Q_{2}$$ be points on the lines $$S P_{1}$$ and $$S P_{2}$$ respectively such that $$P Q_{1}$$ is perpendicular to $$S P_{1}$$ and $$P Q_{2}$$ is perpendicular to $$S P_{2}$$. Then, which of the following is/are TRUE?

A
$$S Q_{1}=2$$
B
$$Q_{1} Q_{2}=\frac{3 \sqrt{10}}{5}$$
C
$$P Q_{1}=3$$
D
$$S Q_{2}=1$$
3
JEE Advanced 2021 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Change Language
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?
A
The triangle PFQ is a right-angled triangle
B
The triangle QPQ' is a right-angled triangle
C
The distance between P and F is 5$$\sqrt 2 $$
D
F lies on the line joining Q and Q'
4
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Change Language
If a chord, which is not a tangent, of the parabola y2 = 16x has the equation 2x + y = p, and mid-point (h, k), then which of the following is(are) possible value(s) of p, h and k?
A
p = $$-$$1, h = 1, k = $$-$$3
B
p = 2, h = 3, k = $$-$$4
C
p = $$-$$2, h = 2, k = $$-$$4
D
p = 5, h = 4, k = $$-$$3
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