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COMEDK2018MathematicsParabola

The ends of the latusrectum of the parabola x²+10 x-16 y+25=0 are

Options

  1. A(3,4),(-13,4)
  2. B(5,-8),(-5,8)
  3. C(3,-4),(13,4)
  4. D(-3,4),(13,-4)

Correct answer

A. (3,4),(-13,4)

Step-by-step solution

Given, equation of parabola is x²+10 x-16 y+25=0 It can be rewritten as (x+5)²=16 y Here a=4 and vertex (-5,0) and focus =(-5,4) So, y -coordinate of ends of latusrectum will be 4 . Putting in equation, we have (x+5)²=16 4=64 x+5= 8 So, x=3,-13 Substituting x in Eq. (i), we get y=4,4 Hence, ends of latusrectum will be (3,4) and (-13,4) .

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