A) A circle
B) An Ellipse
C) A hyperbola
D) A parabola
Correct Answer: D
Solution :
Suppose the centre of circle be\[(h,k)\]. Since it touches the\[y\text{-axis}\], \[\therefore \]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.You need to login to perform this action.
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