Q36 / 90 · JEE Main 2019 (10 Jan Shift 2) · Mathematics

The length of the chord of the parabola $x^{2} = 4 y$ having equation $x - \sqrt{2} y + 4 \sqrt{2} = 0$ is

Correct answer
A
$6 \sqrt{3}$ units
B
$8 \sqrt{2}$ units
C
$2 \sqrt{11}$ units
D
$3 \sqrt{2}$ units

Solution

Solving the equations of the given parabola and the line, we get,

${(\sqrt{2} y - 4 \sqrt{2})}^{2} = 4 y \Rightarrow y^{2} - 10 y + 16 = 0$

$\Rightarrow |y_{1} - y_{2}| = \sqrt{{(y_{1} + y_{2})}^{2} - 4 y_{1} y_{2}} = \sqrt{100 - 64} = 6$

$\Rightarrow$ Length of the chord $= A B = \sqrt{{(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2}} = \sqrt{2 {(y_{1} - y_{2})}^{2} + {(y_{1} - y_{2})}^{2}} = \sqrt{3} |y_{1} - y_{2}|$

$= 6 \sqrt{3}$ units

Hence, the correct answer is option: 'A'.

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The length of the chord of the parabola x2=4y having equation x-2y+42=0 is

Solution

Relevant Questions

The length of the chord of the parabola $x^{2} = 4 y$ having equation $x - \sqrt{2} y + 4 \sqrt{2} = 0$ is