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STD 11 - 10.1 circle and system of circle — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 10.1 circle and system of circle4 Marks
MCQ
A variable circle passes through the fixed point $(2,0)$ and touches the $y$-axis . Then the locus of its centre is
  • A
    A circle
  • B
    An Ellipse
  • C
    A hyperbola
  • ✓
    A parabola
✓

Answer

Correct option: D.
A parabola
d
(d) Suppose the centre of circle be $(h,k)$. Since it touches the $y{\rm{ - axis}}$

$\therefore $ radius of circle = $h$

Now ${(h - 2)^2} + {k^2} = {h^2}$

$ \Rightarrow $${h^2} + 4 - 4h + {k^2} = {h^2}$

$ \Rightarrow $ ${k^2} = 4h - 4$.

Hence the locus of centre is ${y^2} = 4x - 4$, which is a parabola.

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