JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
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:
- A a hyperbola
- B a parabola
- C a circle
- D an ellipse which is not a circle
Answer & Solution
Correct Answer
(B) a parabola
Step-by-step Solution
Detailed explanation
\(x^{2}+y^{2}-8 x-8 y-4=0\) Center \((4,4)\) Radius \(=\sqrt{4 z^{2}+4^{2}+4}=6\) Let centre of the circle is \((\mathrm{h}, \mathrm{k})\) \(\sqrt{(h-4)^{2}+(k-4)^{2}}=(6+k)\) \((h-4)^{2}+(k-4)^{2}=(6+k)^{2}\) \(h^{2}-8 h+16+k^{2}-8 k+16=36+k^{2}+12 k\) \(h^{2}-8 h-20 k-4=0\)…
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