Question

28. If the ratio of the lengths of tangents from a point P to
the circles x2 + y2 + 4x + 3 = 0, x2 + y2 - 6x + 5 = 0 is
1:2 then the locus of P is a circle whose centre is
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Answer 1

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MATHS

The locus of points from which the lengths of the tangents to the two circles x2+y2+4x+3=0 and x2+y2−6x+5=0 are in the ratio 2:3 is a circle with centre

A

(−6,0)

B

(6,0)

C

(0,6)

D

(0,−6)

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ANSWER

Let P(h,k) is an external point.Then length of tangent from P(h,k) to x2+y2+4x=0 is L1

∴L1=h2+k2+4h

And length of tangent from P{h,k) to x2+y2−6x+5=0 is L2

∴L2=h2+k2−6h+5

Given L1:

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