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AP EAMCET20226 Jul 2022Evening ShiftMathematicsParabolaActual

The length of the latusrectum of the parabola (x-2)^2+(y-3)^2= 1 25 (3 x-4 y+7)^2 is

Options

  1. A1 5
  2. B2 5
  3. C3 5
  4. D4 5

Correct answer

B. 2 5

Step-by-step solution

Given, equation of parabola is aligned & (x-2)^2+(y-3)^2= 1 25 (3 x-4 y+7)^2 & 25 [(x-2)^2+(y-3)^2 ]=(3 x-4 y+7)^2 aligned Focus of the parabola =(2,3) Equation of directrix =3 x-4 y+7 Length of latus rectum is twice the perpendicular distance from focus to directrix. L= 2|3 2-4 3+7| 3^2+(-4)^2 =2 [ 6-12+7 5 ]= 2 5

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