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AP EAMCET2002MathematicsParabola

The equation of the parabola with the focus (3,0) and the directrix x+3=0 , is.

Options

  1. Ay^2=3 x
  2. By^2=6 x
  3. Cy^2=12 x
  4. Dy^2=2 x

Correct answer

C. y^2=12 x

Step-by-step solution

Given that focus is S(3,0) , let P(x, y) be any point on the parabola. Directrix is, x+3=0 Also, S P^2=P M^2 aligned & (x-3)^2+(y-0)^2= ( x+3 1 )^2 & (x-3)^2+y^2=(x+3)^2 & y^2=(x+3)^2-(x-3)^2 & =(x+3+x-3)(x+3-x+3) & y^2=2 x 6=12 x aligned

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