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Show that the pair of tangents drawn from (g,f)\, to the circlesx^{2}+y^{2}+2gx+2fy+c=0\, are at right angles if g^{2}+g^{2}+c=0\,

Given circle is x^{2}+y^{2}+2gx+2fy+c=0\,

Equation to the pair of tangents from the point is




For the tangents to be at right angles, the condition is that

coefficient of x^{2}\,+ coefficient of y^{2}\,=0\,

Hence from the above

coefficient of x^{2}=g^{2}-3g^{2}-3f^{2}-c+g^{2}+f^{2}\, coefficient of y^{2}=f^{2}-3g^{2}-3f^{2}-c+2g^{2}+f^{2}\,




Main Page:Geometry:Circles