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

• A. $\frac{x{x}_1}{a^2}-\frac{y{y}_1}{b^2}-1=\frac{x_1^2}{a^2}-\frac{y_1^2}{b^2}-1$
• B. $\frac{x_1{x}^2}{a^2}-\frac{y_1{y}^2}{b^2}-1=\frac{x_1^2}{a^2}-\frac{y_1^2}{b^2}-1$
• C. $\frac{x^2}{a^2}-\frac{y^2}{b^2}=\frac{x_1^2}{a^2}-\frac{y_1^2}{b^2}$
• D. $\frac{x+x_1}{a^2}-\frac{(y+y_1)}{b^2}=\frac{x_1^2}{a^2}-\frac{y_1^2}{b^2}$

Answer 1

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 $S_1\equiv \frac{x{x}_1}{a^2}-\frac{y{y}_1}{b^2}-1andT=\frac{x_1^2}{a^2}-\frac{y_1^2}{b^2}-1.$ Therefore we get option A.