Assertion :The length of latus rectum of the parabola ${(3 x - 4 y + 2)}^{2} = 40 (4 x + 3 y - 5)$ is $16$ . Reason: The length of latus rectum of the parabola ${(y - 2)}^{2} = 16 (x + 3)$ is $16$ .

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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Assertion is incorrect but Reason is correct

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Solution

The correct option is D Assertion is incorrect but Reason is correct
$3 x - 4 y + 2 = 0$ & $4 x + 3 y - 5 = 0$ are $⊥$ er to each other
$∴ 25 {(\frac{3 x - 4 y + 2}{5})}^{2} = 40 (\frac{4 x + 3 y - 5}{5}) \times 5$
$∴$ ${(\frac{3 x - 4 y + 2}{5})}^{2} = 8 (\frac{4 x + 3 y - 5}{5})$
Let $\frac{3 x - 4 y + 2}{5} = Y$ & $\frac{4 x + 3 y - 5}{5} = X$
$∴ Y^{2} = 8 X$
$∴$ Latus rectum $= 8$
Assertion (A) is false
Also the length of latus rectum of $(y - 2)^{2} = 16 (x + 3)$ is 16 which is true.

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