AP EAMCET · Maths · Parabola
The parametric equations of the parabola \(y^2-8 x-4 y-12=0\) are
- A \(x=2+2 t^2, y=-2+4 t\)
- B \(x=2+4 t, y=-2+2 t^2\)
- C \(x=-2+2 t^2, y=2+4 t\)
- D \(x=-2+4 t, y=2+2 t^2\)
Answer & Solution
Correct Answer
(C) \(x=-2+2 t^2, y=2+4 t\)
Step-by-step Solution
Detailed explanation
Given equation of parabola is \(\begin{aligned} y^2-8 x-4 y-12 & =0 \\ y^2-4 y & =8 x+12 \\ (y-2)^2 & =8(x+2) \\ 4 a & =8 \\ a \quad a & =2 \end{aligned}\) \(\therefore\) Parametric equations are \(\begin{aligned} x+2 & =a t^2, y-2=2 a t \\ x & =-2+2 t^2, y=2+4 t \end{aligned}\)…
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