1.

A circle S_(1) passes through the point P(4,-3) and touches the circle S_(2)-=x^(2)+y^(2)-10=0 at the point Q(3,1) on it. If (a,b) is the centre of the director circle of S_(1), then the value of (a)/(b) is less than

Answer»

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Solution :Equation of tangent at Q on `S_(2)` is `3x+y-10=0`.
Equation of circle `S_(1)" is "(x-3)^(2)+(y-1)^(2)+lambda(3x+y-10)`
It passes through `P(4,-3)`.

`1+16+lambda(12-3-10)=0implieslambda=17`
`:.""S_(1)-=x^(2)+y^(2)+45x+15y-160=0`
CENTRE of `S_(1)=0` and its director circle will be same.
`((-45)/(2),(-15)/(2))."":.(a)/(b)=3.`


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