Question

Find the co-ordinates of a point on the parabola $y^2=8x$ whose focal distance is $4?$

• A. $(2,-4)$
• B. $(-2,-4)$
• C. $(2,4)$
• D. $(-2,4)$

Answer 1

Answer: (A), (C)

$(2,-4)$
$(2,4)$

If the co - ordinates of a point on the parabola be $(x,y),$ then its distance from the focus is $SP=a+x$

$\therefore 4=2+x\because 4a=8$ given.

$\therefore x=2$

Hence $y^2=8x=8\times 2=16$

$\therefore y=\pm 4.$
Thus the co - ordinates of the points are $(2,\pm 4)$

Ans: A,C