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

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

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

True

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False

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Solution

The correct option is A
True

This is generally taken as a result. i.e., combined equation of pair of tangents is given by the equation. $S S_{1} = T^{2}$

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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 $x x_{1} + y y_{1} + g (x + x_{1}) + f (y + y_{1}) + c = 0$

What is the length of tangent from a point $P (x_{1}, y_{1})$ to the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0.$

If $(x_{1}, y_{1})$ is a point inside the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ Given two expressions $S_{1}$ and $T_{1}$ such that,

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

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

Then the equation of chord centered at $(x_{1}, y_{1})$ is

Q. The following notation(

S_{1}

) in the circle is used to find the tangent to the circle at point

(x_{1}, y_{1})

S \equiv x^{2} + y^{2} + 2 g x + 2 f y + c

S_{1} \equiv x x_{1} + y y_{1} - g (x + x_{1}) - f (y + y_{1}) + c

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A circle is of the form x2 + y2 + 2gx + 2fy + c = 0 and a pair of tangents are drawn from (x1, y1) to the circle.The combined equation of tangents is SS1 = T2. Where S=x2+y2+2gx+2fy+c S1=x21+y21+2gx1+2fy1+c T=xx1+yy1+g(x+x1)+f(y+y1)+c

The correct option is A True This is generally taken as a result. i.e., combined equation of pair of tangents is given by the equation. SS1 = T2

The correct option is A
True

This is generally taken as a result. i.e., combined equation of pair of tangents is given by the equation. $S S_{1} = T^{2}$