Conic-Sections Question 567
Question: A point moves such that the square of its distance from a straight line is equal to the difference between the square of it distance from the centre of a circle and the square of the radius of the circle. The locus of the point is
Options:
A) A straight line at right angle to the given line
B) A circle concentric with the given circle
C) A parabola with its axis parallel to the given line
D) A parabola with its axis perpendicular to the given line
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Let the given line be the y-axis and the circle to Have the eq. $ x^{2}+y^{2}+2gx+2fy+c=0 $ then according to given condition $ x^{2}+y^{2}+2gx+2fy+c=0 $ then according to given condition $ x^{2}={{(x+g)}^{2}}+{{(y+f)}^{2}}-(g^{2}+f^{2}-c) $
$ \Rightarrow {{(y+f)}^{2}}=-2g( x-\frac{f^{2}-c}{2g} ), $ Which represents a parabola with its axis $ \bot $ to y-axis.
BETA
