two circles touch the x-axis n the line y=mx.they intersect at(9,6) n at one more pt. n the product of their radii is 117/2.then the value of m is....
ans.2√2
-
UP 0 DOWN 0 0 1
1 Answers
1this is easy ..
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 TANθθ
