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Question: The locus of centre of circle of unit radius which rolls out side of the circle x<sup>2</sup> + y<su...

The locus of centre of circle of unit radius which rolls out side of the circle x2 + y2 – 6x + 8y = 0 is –

A

x2 + y2 – 2x – 2y – 24 = 0

B

x2 + y2 – 6x – 8y + 12 = 0

C

x2 + y2 – 6x + 8y – 11 = 0

D

None

Answer

x2 + y2 – 6x + 8y – 11 = 0

Explanation

Solution

x2 + y2 – 6x + 8y = 0

centre (3, – 4) ; radius r1 = 5

Let centre of required circle is c2 ŗ (h, k) ; r2 = 1

C1C2 = r1 + r2

(h–3)2+(k+4)2\sqrt{(h–3)^{2} + (k + 4)^{2}} = 5 + 1

Ž h2 – 6h + 9 + k2 + 8k + 16 = 36

Ž h2 + k2 – 6h + 8k – 11 = 0