Question

The centres of those circles which touch the circle, `x^2+y^2-8x-8y-4=0` , externally and also touch the x-axis, lie on : (1) a circle. (2) an ellipse which is not a circle. (3) a hyperbola. (4) a parabola.
A. an ellipse which is not a circle
B. a hyperbola
C. a parabola
D. a circle

Answer 1

Correct Answer - 3

Let `(h,k)` be the centre of the circle which touch x-axis and `x^(2)+y^(2)-8x-8y-4=0` externally.
`implies `Radius of that circle is `|k|`
`implies (h-4)^(2)+(k-4)^(2)= ( |k| +6)^(2)`
`implies x^(2)-8x-20y-4=0` if `yge0`
and `x^(2)-8x+4y-4=0` if `ylt0`
`implies ` The curve is parabola