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The length of the chord of the parabola $x^2 = 4y$ having the equation $x - \sqrt2y + 4\sqrt2 =0$ is:
Option 1)
$6\sqrt3$
Option 2)
$3\sqrt2$
Option 3)
$8\sqrt2$
Option 4)
$2\sqrt{11}$

Answers (1)

best_answer

Standard equation of parabola -

$x^{2}=4ay$

- wherein

Equation of parabola $x^{2}=4ay$ and chord $x-\sqrt2 y+4\sqrt2=0$

Solve these two equations

$x^{2}=4(\frac{x+4\sqrt2}{\sqrt2})$

$\sqrt2x^{2}=4x+16\sqrt2$

$x_{1}+x_{2}=2\sqrt2\: \: ;\: \: x_{1}x_{2}=-16$

Similarly,

$(\sqrt2y-4\sqrt2)^{2}=4y$

$=>2y^{2}-20y+32=0$

$y_{1}+y_{2}=10\: ;\: y_{1}y_{2}=16$

Length of chord = $\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}$

= $\sqrt{(2\sqrt2)^{2}+64+(10)^{2}-4(16)}$

= $\sqrt{108}$

= $6\sqrt3$

Option 1)
$6\sqrt3$
Option 2)

$3\sqrt2$

Option 3)

$8\sqrt2$

Option 4)

$2\sqrt{11}$

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