The straight lines y- x intersect the parabola y2-8x in points P and Q- then length of PQ is

Explanation for the correct option:Given:y=± xintersect the parabola y^2=8x in points P and Q y^2=8x 0ex0exy^2=± 8y [∵ y=± x]0ex0exy(y± 8)=00ex0exy=0,± ...

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Standard XII

Mathematics

Focal Chord of Ellipse

The straight ...

Question

The straight lines $y = \pm x$ intersect the parabola $y^{2} = 8 x$ in points $P$ and $Q,$ then length of $P Q$ is

$4$

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$4 \sqrt{2}$

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$8$

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$16$

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Solution

The correct option is D
$16$

Explanation for the correct option:
Given:
$y = \pm x$ intersect the parabola $y^{2} = 8 x$ in points $P$ and $Q$
$y^{2} = 8 x y^{2} = \pm 8 y [∵ y = \pm x] y (y \pm 8) = 0 y = 0, \pm 8 ∴ P (8, 8), Q = (8, - 8)$
Length of $P Q = \sqrt{{(8 + 8)}^{2} + (8 + {(- 8)}^{2}}$ [Distance formula]
$P Q = \sqrt{16^{2} + 0^{2}} = 16$
Hence the correct option is option D.

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The straight lines y=±x intersect the parabola y2=8x in points P and Q, then length of PQ is

The correct option is D 16Explanation for the correct option:Given:y=±xintersect the parabola y2=8x in points P and Q y2=8xy2=±8y∵y=±xy(y±8)=0y=0,±8∴P(8,8),Q=(8,-8) Length of PQ=(8+8)2+(8+(-8)2 [Distance formula] PQ=162+02=16Hence the correct option is option D.

The straight lines $y = \pm x$ intersect the parabola $y^{2} = 8 x$ in points $P$ and $Q,$ then length of $P Q$ is