Equation of the pair of tangents drawn from the origin to the circle x2-y2-2 g x-2 f y-c-0 isA- g x-f y2-x2-y2B- g x-f y-cx2-y2C- g x-f y2-c2x2-y2D- g x-f y2-cx2-y2

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Byju's Answer

Standard XII

Mathematics

Chord of Contact

Equation of t...

Question

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

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Solution

The correct option is D

Equation of pair of tangents is $S S_{1} = T^{2}$ ,

where $T = x x_{1} + y y_{1} + g (x + x_{1}) + f (y + y_{1}) + c$

$\Rightarrow c (x^{2} + y^{2} + 2 g x + 2 f y + c) = (g x + f y + c)^{2}$

$\Rightarrow c (x^{2} + y^{2}) = (g x + f y)^{2}$

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Similar questions

Q. Locus of mid point of chords of

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

that pass through the origin, is

A circle is of the form $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ and a pair of tangents are drawn from $(x_{1}, y_{1})$ to the circle.The combined equation of tangents is $S S_{1} = T^{2} .$

Where $S = x^{2} + y^{2} + 2 g x + 2 f y + c$

$S_{1} = x_{1}^{2} + y_{1}^{2} + 2 g x_{1} + 2 f y_{1} + c$

$T = x x_{1} + y y_{1} + g (x + x_{1}) + f (y + y_{1}) + c$

A circle is of the form $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ and a pair of tangents are drawn from $(x_{1}, y_{1})$ to the circle.The combined equation of tangents is $S S_{1} = T^{2} .$

Where $S = x^{2} + y^{2} + 2 g x + 2 f y + c$

$S_{1} = x_{1}^{2} + y_{1}^{2} + 2 g x_{1} + 2 f y_{1} + c$

$T = x x_{1} + y y_{1} + g (x + x_{1}) + f (y + y_{1}) + c$

The equation of tangent to the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ at its point $(x_{1}, y_{1})$ is given by $x x_{1} + y y_{1} + g (x + x_{1}) + f (y + y_{1}) + c = 0$

Q. Equation of the pair of tangents drawn from the origin to the circle

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

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Equation of the pair of tangents drawn from the origin to the circle x2+y2+2gx+2fy+c=0 is

The correct option is D Equation of pair of tangents is SS1=T2, where T=xx1+yy1+g(x+x1)+f(y+y1)+c ⇒c(x2+y2+2gx+2fy+c)=(gx+fy+c)2 ⇒c(x2+y2)=(gx+fy)2

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

The correct option is D

Equation of pair of tangents is $S S_{1} = T^{2}$ ,

where $T = x x_{1} + y y_{1} + g (x + x_{1}) + f (y + y_{1}) + c$

$\Rightarrow c (x^{2} + y^{2} + 2 g x + 2 f y + c) = (g x + f y + c)^{2}$

$\Rightarrow c (x^{2} + y^{2}) = (g x + f y)^{2}$