Question

The focal distance of a point on the parabola $(x-1{)}^2=16(y-4)$ is $8.$ Find the co-ordinates.

• A. only $(-7,8)$
• B. only $(9,8)$
• C. only $(-9,8)$
• D. both A and B

Answer 1

Answer: (D)

both A and B

Focus of the given parabola is $S\equiv (1,4+4)=(1,8)$
Any point on the given parabola is $P(1+8t,4+4t^2)$
Thus focal distance $SP=\sqrt{64t^2+(4t^2-4{)}^2}=4t^2+4=8$ (given)
$\Rightarrow t=\pm 1$ Hence P is $(9,8)$ or $(-7,8)$