The equation(s) to common tangent(s) to the two hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}}

Question

The equation(s) to common tangent(s) to the two hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ and $\frac{y^{2}}{a^{2}} - \frac{x^{2}}{b^{2}} = 1$ is/are:

Accepted Answer

Sol. (a, b, c, d)Equation of tangent of $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$$$\begin{array}{r} y = mx \pm \sqrt{a^{2}m^{2} - b^{2}}\#(1) \end{array}$$∵ (1) is tangent to $\frac{x^{2}}{\left( - b^{2} \right)} - \frac{y^{2}}{\left( - a^{2} \right)} = 1$$${\Rightarrow a^{2}m^{2} - b^{2} = - b^{2}m^{2} - \left( - a^{2} \right) }{\Rightarrow m^{2} = 1 }$$∴ Equation of common tangents are $y = \pm x \pm \sqrt{a^{2} - b^{2}}$

Question

Options

Solution

More Hyperbola Questions