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Grade: 12
two circles touch x axis and line y=mx .they meet at (9,6) and at one more point the product of their radii is 117/2 then value of m is
2 years ago

Answers : (1)

23372 Points

just take centre of circle (h,r) with r as its radius as it touches the x - axis

then we can write

(x-h)2 + (y-r)2=r2

further as the circle also touches y=mx

let us take tanθ=m then we have r=htan(θ/2)

substituting the value of h in the equation we get a quadratic in r ..

thus two possible radii and hence two circles

as both the circles pass through 9,6 this point should satisfy the equation ..

now substitute x=9,y=6

apply product of roots =c/a you will get tan(θ/2) AND HENCE TANθ

2 years ago
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