1
JEE Advanced 2023 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2 Let $T_1$ and $T_2$ be two distinct common tangents to the ellipse $E: \frac{x^2}{6}+\frac{y^2}{3}=1$ and the parabola $P: y^2=12 x$. Suppose that the tangent $T_1$ touches $P$ and $E$ at the points $A_1$ and $A_2$, respectively and the tangent $T_2$ touches $P$ and $E$ at the points $A_4$ and $A_3$, respectively. Then which of the following statements is(are) true?
A
The area of the quadrilateral $A_1 A_2 A_3 A_4$ is 35 square units
B
The area of the quadrilateral $A_1 A_2 A_3 A_4$ is 36 square units
C
The tangents $T_1$ and $T_2$ meet the $x$-axis at the point $(-3,0)$
D
The tangents $T_1$ and $T_2$ meet the $x$-axis at the point $(-6,0)$
2
JEE Advanced 2022 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2 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 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 2020 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2 Let a and b be positive real numbers such that a > 1 and b < a. Let P be a point in the first quadrant that lies on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. Suppose the tangent to the hyperbola at P passes through the point (1, 0), and suppose the normal to the hyperbola at P cuts off equal intercepts on the coordinate axes. Let $$\Delta$$ denote the area of the triangle formed by the tangent at P, the normal at P and the X-axis. If e denotes the eccentricity of the hyperbola, then which of the following statements is/are TRUE?
A
$$1 < e < \sqrt 2$$
B
$$\sqrt 2 < e < 2$$
C
$$\Delta = {a^4}$$
D
$$\Delta = {b^4}$$
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