Question

A point moves such that the square of its distance from a straight line is equal to the difference between the square of its distance from the centre of a circle and the square of radius of the circle. The locus of the point is

• A. a straight line at right angle to the given line
• B. a circle concentric with the given cirlce
• C. a parabola with its axis parallel to the given line
• D. a parabola with its axis perpendicular to the given line.

Answer 1

The correct option is D a parabola with its axis perpendicular to the given line.

$(h-p{)}^2=(h-a{)}^2+(k-c{)}^2-r^2$
$(h-p{)}^2=(h-a{)}^2+(k-L{)}^2$
LTH a parabola
because distance from a fixed line (directice) and a fixed point (locus) is equal
then the locus of the point is parabola.