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Let `2 x^2 + y^2 - 3xy = 0` be the equation of pair of tangents drawn from the origin to a circle of radius 3, with center in the first quadrant. If A is the point of contact. Find OA |
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Answer» `2x^2+y^2-3xy=0` `y^2-2xy-xy+2x^2=0` `y(y-2x)-x(y-2x)=0` `(y-x)(y-2x)=0` `y=x` or `y=2x` `tantheta=|(2-1)/(1+2)|=1/3` `(2tantheta)/(1-tan^2theta)=1/3` `6tantheta=1-tan^2theta` `tan^2theta+6tantheta+1=0` `tantheta=(-6pmsqrt32)/2` `=-3pm2sqrt2` `=-3-2sqrt2,|-3+2sqrt2|` `tantheta=(AC)/(OA)` `OA=3/(3-2sqrt2)*(3+2sqrt2)/(3+2sqrt2)` `OA=3(3+2sqrt2)`. |
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