Questions
A variable circle passes through the fixed point (2, 0) and touches the y-axis. Then, the locus of its centre, is
a
a parabola
b
a circle
c
an ellipse
d
a hyperbola
detailed solution
Correct option is A
Let the variable circle bex2+y2+2gx+2fy+c=0 ... (i)It passes through (2, 0) and touches y-axis.∴ 4+4g+c=0 and c=f2⇒ 4+4y+f2=0Hence, the locus of the centre (- g, - f) of circle (i) is4−4x+y2=0⇒ y2=4(x−1), which is a parabola.Talk to our academic expert!
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