Q92 / 160 · AP EAMCET 2022 (06 Jul Shift 1) · Mathematics

The parabola with focus at $(4,-3)$ and vertex at $(4,-1)$ is

  • A
    $\mathrm{x}^2+8 \mathrm{x}+6 \mathrm{y}+22=0$
  • B
    $x^2-8 x-10 y+6=0$
  • C
    $x^2-8 x-16 y=0$
  • Correct answer
    D
    $x^2-8 x+8 y+24=0$

Solution

Since points $(4,-3)$ and $(4,-1)$ lie on the line $x=$ 4. So axis of parabola is the line $x=4$. Focus of the parabola lies below the vertex. So the parabola is downwards. $\therefore \mathrm{a}=\sqrt{(4-4)^2+(-3+1)^2}$ (distance between focus and vertex. $$ =2 $$ $\therefore$ Equation of parabola is $$ \begin{aligned} & (x-4)^2=-4(2)(y+1) \\ & \Rightarrow x^2-8 x+8 y+24=0 \end{aligned} $$

Hence, the correct answer is option: 'D'.

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