Intersection of a line and a parabola - class-XI

Question 1 Multiple Choice (Single Answer)

The length of the chord of the parabola $y^2 = 4x$ which passes through the vertex and makes $30^o$ angle with x-axis is

$\dfrac{\sqrt{3}}{2}$
$\dfrac{3}{2}$
$8\sqrt{3}$
$\sqrt{3}$

Question 2 Multiple Choice (Single Answer)

Length of chord of parabola ${y}^{2}=4ax$ whose equation is $y-\sqrt {2}x+4\sqrt {2}a=0$

$2\sqrt {11}a$
$4\sqrt {2}a$
$8\sqrt {2}a$
$6\sqrt {3}a$

Question 3 Multiple Choice (Single Answer)

The length of the chord $y = x - 2$ intercepted by the parabola ${ y }^{ 2 }=4(x-1)$ is

$4$
$\dfrac { 16 }{ 3 } $
$\dfrac { 3 }{ 16 } $
$\dfrac { 1 }{ 4 } $

Question 4 Multiple Choice (Single Answer)

The length of normal chord to the parabola $y^{2} = 4x$ which subtends a right angle at the vertex is

$6\sqrt {3}$
$6\sqrt {2}$
$7\sqrt {2}$
$7\sqrt {3}$

Question 5 Multiple Choice (Single Answer)

The number of focal chord(s) of length $\dfrac{4}{7}$ in the parabola $7y^2 = 8x$ is

$1$
$0$
infinite
none of these

Question 6 Multiple Choice (Single Answer)

Find the length of the chord of the parabola $y^2, =, 8x$, whose equation is $x + y = 1$.

$8 \sqrt{3}$
$4 \sqrt {3}$
$2 \sqrt {3}$
$\sqrt {3}$

Question 7 Multiple Choice (Single Answer)

The length of the chord of the parabola $x^2 = 4y $ passing through the vertex and having slope $cot \alpha $ is

$4 \cos \alpha . cosec^2\alpha$
$ 4a \tan \alpha \sec \alpha $
$4 \sin \alpha . \sec^2 \alpha $
none of these

Question 8 Multiple Choice (Single Answer)

Let $AB$ be a chord of the parabola $y^{2}=4ax$.If the pole of $AB$ with respect to the parabola be $\left ( 2a,3a \right )$ then the length of $AB$ is

$\sqrt{13}a$
$4a$
$5a$
$2\sqrt{3}a$

Question 9 Multiple Choice (Single Answer)

The condition that the straight line $\displaystyle lx + my + n = 0$ touches the parabola $\displaystyle x^2 = 4ay$ is

$\displaystyle bn = am^2$
$\displaystyle al^2 - mn = 0$
$\displaystyle ln = am^2$
$\displaystyle am = ln^2$

Question 10 Multiple Choice (Single Answer)

The length of the chord of the parabola $y^2 = x$ which is bisected at the point $(2, 1)$ is

$2 \sqrt{3}$
$4 \sqrt{3}$
$3 \sqrt{2}$
$2 \sqrt{5}$

Question 11 Multiple Choice (Single Answer)

If $2$ and $3$ are the length of the segments of any focal chord of a parabola $y^2 = 4ax$, then value of $2a$ is

$\dfrac{13}{5}$
$\dfrac{12}{5}$
$\dfrac{11}{5}$
none of these

Question 12 Multiple Choice (Single Answer)

If the line $y- \sqrt x +3 = 0$ cuts the parabola $y^2 = x + 2$ at $A$ and $B$, and if $P$ $(3,\ 0)$, then $PA.PB$ is equal to

$\dfrac{2(\sqrt 3+2)}{3}$
$\dfrac{4\sqrt 3}{2}$
$\dfrac{4(2-\sqrt 3)}{3}$
$\dfrac{4(\sqrt3+2)}{3}$

Intersection of a line and a parabola - class-XI

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