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Find the length of the latus rectum of the equation :
169{(x-1)^2-(y-3)^2}=(5x-12y+17)^2
169{(X-1)2-(Y-3)2}=(5X-12Y+17)2
13{(X-1)2-(Y-3)2}1/2=(5X-12Y+17)
13{(X-1)2-(Y-3)2}1/2=13(5X-12Y+17)/(52+122)1/2
{(X-1)2-(Y-3)2}1/2
......................... =1 (ESSENTRICITY OF PARABOLA IS 1 ) THIS IS A GENERAL FORM OF A PARABOLA WITH FOCUS (1,3) AND EQUATION
(5X-12Y+17)/(52+122)1/2 OF DIRECTRIX AS (5X-12Y+17)
NOW PERPENDICULAR DISTANCE BETWEEN THE FOCUS AND THE DIRECTRIX IS = MODULUS OF [1*5-3*12+17]/{(52+122)1/2 }
DISTANCE =14/13 THEREFORE FROM THE DIAGRAM 2X=14/13 LENGTH OF LATUS RECTUM IS 4X THEREFORE LENGTH=28/13................ANSWER
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