Latus rectum of the parabola whose focus is $(3, 4)$ and whose tangent at vertex has the equation $x + y = 7 + 5 \sqrt{2}$ is -

5

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10

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20

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15

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Solution

The correct option is A $20$
Length of latus rectum will be four times the distance of focus from tangent at vertex
Length of latus rectum is $4 \times \frac{| 3 + 4 - 7 - 5 \sqrt{2} |}{\sqrt{1 + 1}} = 20$

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Latus rectum of the parabola whose focus is (3,4) and whose tangent at vertex has the equation x + y = 7 + 5√2 is ?

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