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If the abscissa and ordinates of two points `Pa n dQ`are the roots of the equations `x^2+2a x-b^2=0`and `x^2+2p x-q^2=0`, respectively, then find the equation of the circle with `P Q`as diameter. |
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Answer» Let `x_(1),x_(2)` and `y_(1),y_(2)` be the roots of `x^(2)+2ax-b^(2)=0` and `x^(2)+2px-q^(2)=0`, respectively. Then, `x_(1)+x_(2)=-2a,x_(1)x_(2)=-b^(2)` and `y_(1)+y_(2)=-2p,y_(1)y_(2)=-q^(2)` The equation of the circle with `P(x_(1),y_(1))` and `Q(x_(2),y_(2))` as the endpoints of diameter is `(x-x_(1))(x-x_(2))+(y-y_(1))(y-y_(2))=0` or `x^(2)+y^(2)-x(x_(1)+x_(2))-y(y_(1)+y_(2))+x_(1)x_(2)+y_(1)y_(2)=0` or `x^(2)+y^(2)+2ax+2py-b^(2)-q^(2)=0` |
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