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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