New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Parabola question

2010 · Shift 1 · Q35

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Advanced
Mathematics
Parabola
2010 · Shift 1 · Q35

Parabola question

2010 · Shift 1 · Q35

JEE AdvancedMathematicsParabolaMultiple correct+4 / −1

Let

A

and

B

be two distinct points on the parabola

{y^2} = 4x

. If the axis of the parabola touches a circle of radius

r

having

AB

as its diameter, then the slope of the line joining

A

and

B

can be

A
$- {1 \over r}$
B
${1 \over r}$
C
${2 \over r}$
D
$- {2 \over r}$

More from Parabola

The tangent $P T$ and the normal $P N$ to the parabola $y^{2} = 4 a x$ at a point $P$ on it meet its axis at points $T$ and $N$ , respectively. The locus of the centroid of the triangle $P T N$ is a parabola whose2009 · Multiple correct
The locus of the orthocentre of the triangle formed by the lines $(1 + p) x - p y + p (1 + p) = 0, (1 + q) x - q y + q (1 + q) = 0$ and $y = 0$ , where $p e q$ , is :2009 · MCQ
The tangent to the curve $y = e^{x}$ drawn at the point ( $c, e^{c}$ ) intersects the line joining the points ( $c - 1, e^{c - 1}$ ) and ( $c + 1, e^{c + 1}$ )2007 · MCQ
Consider the circle $x^{2} + y^{2} = 9$ and the parabola $y^{2} = 8 x$ . They intersect at P and Q in the first and the fourth quadrants, respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents to the parabola…2007 · MCQ
Consider the circle $x^{2} + y^{2} = 9$ and the parabola $y^{2} = 8 x$ . They intersect at P and Q in the first and the fourth quadrants, respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents to the parabola…2007 · MCQ
Consider the circle $x^{2} + y^{2} = 9$ and the parabola $y^{2} = 8 x$ . They intersect at P and Q in the first and the fourth quadrants, respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents to the parabola…2007 · MCQ
Let $S$ denote the locus of the mid-points of those chords of the parabola $y^{2} = x$ , such that the area of the region enclosed between the parabola and the chord is $\frac{4}{3}$ . Let $R$ denote the region lying in the first…2025 · Multiple correct
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…2024 · Multiple correct