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Question Number 209041 by alcohol last updated on 30/Jun/24

Commented by alcohol last updated on 30/Jun/24

find r

findr

Commented by mr W last updated on 01/Jul/24

Answered by mr W last updated on 01/Jul/24

say touching point on y=x^2  at P(p, p^2 )  center of circle C(2−r, 2−r)  tan θ=2p  2−r=p+r sin θ ⇒2−r=p+((2pr)/( (√(1+4p^2 ))))  ⇒r=((2−p)/(1+((2p)/( (√(1+4p^2 ))))))  2−r=p^2 −r cos θ ⇒2−r=p^2 −(r/( (√(1+4p^2 ))))  ⇒r=((2−p^2 )/(1−(1/( (√(1+4p^2 ))))))  ((2−p^2 )/(1−(1/( (√(1+4p^2 ))))))=((2−p)/(1+((2p)/( (√(1+4p^2 ))))))  ⇒p≈1.3328, r≈0.3446

saytouchingpointony=x2atP(p,p2)centerofcircleC(2r,2r)tanθ=2p2r=p+rsinθ2r=p+2pr1+4p2r=2p1+2p1+4p22r=p2rcosθ2r=p2r1+4p2r=2p2111+4p22p2111+4p2=2p1+2p1+4p2p1.3328,r0.3446

Commented by mr W last updated on 30/Jun/24

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