The length of the latus rectum of the parabola
$169 {(x - 1)^{2} + (y - 3)^{2}} = (5 x - 12 y + 17)^{2}$ is

\frac{14}{11}

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\frac{12}{13}

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\frac{28}{13}

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none of these

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Solution

The correct option is C $\frac{28}{13}$
Given parabola may be written as, $(x - 1)^{2} + (y - 3)^{2} = {(\frac{5 x - 12 y + 17}{\sqrt{5^{2} + 12^{2}}})}^{2}$

Thus focus of the parabola is $(1, 3)$ and directrix is $5 x - 12 y + 17$

Now distance between directrix to the focus is $= \frac{5 (1) - 12 (3) + 17}{\sqrt{5^{2} + 12^{2}}} = \frac{14}{13}$

Hence length of latus rectum of the parabola is $= 2 \times \frac{14}{13} = \frac{28}{13}$

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Similar questions

169 {(x - 1)^{2} + (y - 3)^{2}} = (5 x - 12 y + 17)^{2}

169 {(x - 1)^{2} + (y - 3)^{2}} = (5 x - 12 y + 17)^{2}

169 [(x - 1)^{2} + (y - 3)^{2}] = (5 x - 12 y + 17)^{2}

(a) If the equation $λ x^{2} 4 x y + y^{2} + λ x + 3 y + 2 = 0$ represents a parabola then find

(b) Find the length of latus rectum of the parabola $169 {(x - 1)^{2} + {(y - 3)}^{2}} = (5 x - 12 y + 17)^{2} .$

169 {{(x - 1)}^{2} + {(y - 3)}^{2}} = {(5 x - 12 y + 17)}^{2}

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