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AP EAMCET202017 Sep 2020Morning ShiftMathematicsParabolaActual

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

Options

  1. A( 14 13 )
  2. B( 12 13 )
  3. C( 28 13 )
  4. D( 56 13 )

Correct answer

C. ( 28 13 )

Step-by-step solution

Given parabola, ( array cc & 169 [(x-1)^2+(y-3)^2 ]=(5 x-12 y+17)^2 & (x-1)^2+(y-3)^2= ( 5 x-12 y+17 13 )^2 & (S P=P M) array ) Here, focus is (S(1,3) ) and directrix ((5 x-12 y+17)=0 ) ( ) Distance of focus from directrix ( aligned & 2 a= | 5-36+17 25+144 | & 2 a= 14 13 & Latusrectum =4 a= 28 13 aligned )

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