Geo4.69

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Find the equation of the pair of tangents drawn from the point (4,3)\, to the circle x^{2}+y^{2}-2x-4y=0\, and hence find the angle between them.

Given circle is x^{2}+y^{2}-2x-4y=0\,

The equation of the pair of tangents is

[S_{1}]^{2}=SS_{{11}}\,

(x(4)+y(3)-1(x+4)-2(y+3)^{2}=(x^{2}+y^{2}-2x-4y)(4^{2}+3^{2}-2(4)-4(3))\,

(3x+y-10)^{2}=5x^{2}+5y^{2}-10x-20y\,

9x^{2}+y^{2}+100+6xy-20y-60x=5x^{2}+5y^{2}-10x-20y\,

4x^{2}+6xy-4y^{2}-50x+100=0\,

Here in the equation,sum of the coefficient of x^{2},y^{2}\, is zero, hence the angle

between the tangents is 90^{\circ }\,

Main Page:Geometry:Circles