Answer:

Explanation:
Any point on a given parabola is equidistant from focus and directrix.
Given:
Focus of the parabola is at
.
Directrix of the parabola is
.
Let
be any point on the parabola. Then, from the definition of a parabola,
Distance of
from focus = Distance of
from directrix.
Therefore,

Squaring both sides, we get
![(x-2)^(2)+(y-8)^(2)=(y-10)^(2)\\(x-2)^(2)=(y-10)^(2)-(y-8)^(2)\\(x-2)^(2)=(y-10+y-8)(y-10-(y-8))...............[\because a^(2)-b^(2)=(a+b)(a-b)]\\(x-2)^(2)=(2y-18)(y-10-y+8)\\(x-2)^(2)=2(y-9)(-2)\\(x-2)^(2)=-4(y-9)\\y-9=-(1)/(4)(x-2)^(2)\\y=-(1)/(4)(x-2)^(2)+9](https://img.qammunity.org/2020/formulas/mathematics/middle-school/cwu6qo4b36cyxaku0jy1x64coo0akcmxnw.png)
Hence, the equation of the parabola is
.