The equation of the chord of the circle x2-y2-a2 having x1- y1 as its mid-point isA- x1-y1-aB- x y1-y x1-a2C- x1-y y1-a2D- x1-y y1-x12-y12

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Standard XII

Mathematics

Radical Axis

The equation ...

Question

The equation of the chord of the circle $x^{2} + y^{2} = a^{2}$ having $(x_{1}, y_{1})$ as its mid-point is

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Solution

The correct option is C

T = $S_{1}$ is the equation of desired chord, hence

$x x_{1} + y y_{1} - a^{2} = x_{1}^{2} + y_{1}^{2} - a^{2} \Rightarrow x x_{1} + y y_{1} = x_{1}^{2} + y_{1}^{2}$

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Similar questions

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

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

The equation of the tangent at $(x_{1}, y_{1})$ to a curve $y^{2} = 4 a x$ at a point $(x_{1}, y_{1})$ is given by $y y_{1} = 2 a (x + x_{1})$

What is the equation of chord of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ whose middle point is $(x_{1}, y_{1})$ ? You are given. $T = \frac{x x_{1}}{a^{2}} + \frac{y y_{1}}{b^{2}} - 1 a n d S_{1} \frac{x_{1}^{2}}{a^{2}} + \frac{y_{1}^{2}}{b^{2}} - 1$

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

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

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

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The equation of the chord of the circle x2+y2=a2 having (x1,y1) as its mid-point is

The correct option is C T = S1 is the equation of desired chord, hence xx1+yy1−a2=x21+y21−a2⇒xx1+yy1=x21+y21

The equation of the chord of the circle $x^{2} + y^{2} = a^{2}$ having $(x_{1}, y_{1})$ as its mid-point is

The correct option is C

T = $S_{1}$ is the equation of desired chord, hence

$x x_{1} + y y_{1} - a^{2} = x_{1}^{2} + y_{1}^{2} - a^{2} \Rightarrow x x_{1} + y y_{1} = x_{1}^{2} + y_{1}^{2}$