Equation of chord of the hyperbola x2-a2-y2-b2-1 whose mid point is x1- y1 is given by

The correct option is A xx_1/a^2 yy_1/b^2 1 = x_1^2/a^2 y_1^2/b^2 1Equation of chord of the hyperbola x^2/a^2 y^2/b^2 = 1 whose mid point is (x_1, y_ ...

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Byju's Answer

Standard XII

Mathematics

Chord with a Given Mid Point : Hyperbola

Equation of c...

Question

Equation of chord of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ whose mid point is $(x_{1}, y_{1})$ is given by

\frac{x x_{1}}{a^{2}} - \frac{y y_{1}}{b^{2}} - 1 = \frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} - 1

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\frac{x_{1} x^{2}}{a^{2}} - \frac{y_{1} y^{2}}{b^{2}} - 1 = \frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} - 1

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\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = \frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}}

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\frac{x + x_{1}}{a^{2}} - \frac{(y + y_{1})}{b^{2}} = \frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}}

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Solution

The correct option is A $\frac{x x_{1}}{a^{2}} - \frac{y y_{1}}{b^{2}} - 1 = \frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} - 1$
Equation of chord of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ whose mid point is $(x_{1}, y_{1})$ is given by T = $S_{1}$ where $S_{1} \equiv \frac{x x_{1}}{a^{2}} - \frac{y y_{1}}{b^{2}} - 1 a n d T = \frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} - 1.$ Therefore we get option A.

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Similar questions

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. $T = \frac{x x_{1}}{a^{2}} + \frac{y y_{1}}{b^{2}} - 1 a n d S_{1} \frac{x_{1}^{2}}{a^{2}} + \frac{y_{1}^{2}}{b^{2}} - 1$

Q. The equation of the chord joining two points

(x_{1}, y_{1})

and

(x_{2}, y_{2})

on the rectangular hyperbola

x y = c^{2}

Q. The equation of the chord joining two points

(x_{1}, y_{1}) a n d (x_{1}, y_{1}) o n t h e r e c t a n g u l a r h y p e r b o l a x y = c^{2} i s

Q. The equation of polar of the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

with respect to the pole

(x_{1}, y_{1})

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Equation of chord of the hyperbola x2a2−y2b2=1 whose mid point is (x1,y1) is given by

The correct option is A xx1a2−yy1b2−1=x21a2−y21b2−1Equation of chord of the hyperbola x2a2−y2b2=1 whose mid point is (x1,y1) is given by T = S1 where S1≡xx1a2−yy1b2−1 and T=x21a2−y21b2−1. Therefore we get option A.

Equation of chord of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ whose mid point is $(x_{1}, y_{1})$ is given by