Solve the problem.
-The parabola $y ^ { 2 } = - 20 x$ is shifted 7 units down and 2 units to the right. Find the focus and directrix of the new parabola.
A) Focus: (-7, -3); Directrix: y = 7
B) Focus: (7, -7); Directrix: x = 7
C) Focus: (-3, -7); Directrix: x = -3
D) Focus: (-3, -7); Directrix: x = 7

Question

Quizplus · Accepted Answer

The standard form of the given parabola is $y^2=-20x \Longrightarrow 4p=-20 \Longrightarrow p=-5$ (focus is at $(-5,0)$).

After the shift, the parabola becomes $y^2=-20(x-2)-7 \Longrightarrow y^2=-20(x-2)+49 \Longrightarrow 4p=-20 \Longrightarrow p=-5$ (focus becomes at $(-5+2,-7)=(-3,-7)$).

Thus, the focus is at $(-3,-7)$ and the directrix is a vertical line $p$ units to the right of the vertex, so it is $x=2+(-5)=-3$. Therefore, choice D is correct.

Solve the Problem y2=−20xy ^ { 2 } = - 20 xy2=−20x

Solve the Problem $y ^ { 2 } = - 20 x$