The length of the latus rectum of the parabola 169 [ ( x - 1 ) 2 + ( y - 3 ) 2 ] = ( 5 x - 12 y + 17 ) 2 is

Question

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

Smart Achievers · Accepted Answer

(2)

$Given parabola is$ ${(x - 1)}^{2} + {(y - 3)}^{2} = {(\frac{5 x - 12 y + 17}{13})}^{2}$

$Focus = (1, 3),$ $directrix is$

$5 x - 12 y + 17 = 0$

$∴$ $Length of latus rectum = 2$ $| \frac{5 - 36 + 17}{13} |$ $= \frac{28}{13}$

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