1
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
$$S Q_{2}=1$$
2
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'
3
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
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
4
JEE Advanced 2016 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Let $$P$$ be the point on the parabola $${y^2} = 4x$$ which is at the shortest distance from the center $$S$$ of the circle $${x^2} + {y^2} - 4x - 16y + 64 = 0$$. Let $$Q$$ be the point on the circle dividing the line segment $$SP$$ internally. Then
A
$$SP = 2\sqrt 5 $$
B
$$SQ:QP = \left( {\sqrt 5 + 1} \right):2$$
C
the $$x$$-intercept of the normal to the parabola at $$P$$ is $$6$$
D
the slope of the tangent to the circle at $$Q$$ is $${1 \over 2}$$
JEE Advanced Subjects