Assertion :Length of the common chord of the parabola $y^{2} = 8 x$ and the circle $x^{2} + y^{2} = 9$ is less than the length of the latus rectum of the parabola. Reason: If the vertex of a parabola lies at the point $(a, 0)$ and the directrix is $x + a = 0$ , then the focus of the parabola is at the point $(2 a, 0)$ .

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is C Assertion is correct but Reason is incorrect
Points of intersection are given by
$x^{2} + 8 x - 9 = 0, x > 0 \Rightarrow x = 1, y = \pm 2 \sqrt{2}$
The length of the latus rectum is $4 \sqrt{2}$ . And hence, assertion is true.
Reason is false as the vertex is equidistant from the focus and the directrix.

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Assertion :Length of the common chord of the parabola y2=8x and the circle x2+y2=9 is less than the length of the latus rectum of the parabola. Reason: If the vertex of a parabola lies at the point (a,0) and the directrix is x+a=0, then the focus of the parabola is at the point (2a,0).

The correct option is C Assertion is correct but Reason is incorrectPoints of intersection are given by x2+8x−9=0,x>0⇒x=1,y=±2√2The length of the latus rectum is 4√2. And hence, assertion is true.Reason is false as the vertex is equidistant from the focus and the directrix.