Find the equation of the curve on which the point $P$ lies. The distance between point $P$ and the point ( 0 ,
11) is $\frac { 11 } { 7 }$ of the distance between point $P$ and the line $y = - 7$.
A) $\quad 49 x ^ { 2 } - 72 y ^ { 2 } + 2,772 y = 0$
B) $\quad 2,772 x ^ { 2 } - 72 y ^ { 2 } - 49 y = 0$
C) $\quad 49 x ^ { 2 } - 72 y ^ { 2 } - 2,772 y = 0$
D) $\quad 49 x ^ { 2 } - 72 y ^ { 2 } - 2,772 y = 50$
E) none of these

Question

Quizplus · Accepted Answer

Let the coordinates of point $P$ be $(x,y)$. Using the distance formula, we have:

$\sqrt{x^2+(y-11)^2}=\frac{11}{7}\cdot\frac{|y+7|}{\sqrt{1^2+0^2}}$

Squaring both sides and simplifying gives:

$49x^2-72y^2-2,772y=0$

Therefore, the equation of the curve on which point $P$ lies is $\boxed{	extbf{(C) }49x^2-72y^2-2,772y=0}$.

Find the Equation of the Curve on Which the Point PPP

Find the Equation of the Curve on Which the Point $P$