question_answer

The centres of those circles which touch the circle, \[{{\text{x}}^{\text{2}}}+{{\text{y}}^{\text{2}}}\text{8x}\text{8y}\text{4}=0,\]externally and also touch the x-axis, lie on :- [JEE Main Solved Paper-2016 ]

A)  A parabola                        

B) A circle

C) An ellipse which is not a circle

D) A hyperbola

Correct Answer: A

Solution :

                Consider line L at a dist. of 6 unit below x axis \[\Rightarrow \]\[PC=PQ\]\[\Rightarrow \]lies on a parabola for which C is focus and L is directrix