Equation of pair of tangents drawn from origin to circle {x^2} + {y^2} + 2gx + 2fy + c = 0 is

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10-1.Circle and System of Circles

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Equation of the pair of tangents drawn from the origin to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$ is

A

$gx + fy + c({x^2} + {y^2})$

B

${(gx + fy)^2} = {x^2} + {y^2}$

C

${(gx + fy)^2} = {c^2}({x^2} + {y^2})$

D

${(gx + fy)^2} = c({x^2} + {y^2})$

Solution

(d) Equation of pair of tangents is $S{S_1} = {T^2}$,

where $T = x{x_1} + y{y_1} + g(x + {x_1}) + f(y + {y_1}) + c$

$\Rightarrow c({x^2} + {y^2} + 2gx + 2fy + c) = {(gx + fy + c)^2}$

$ \Rightarrow c({x^2} + {y^2}) = {(gx + fy)^2}$.

Standard 11

Mathematics

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