The locus of a point $P(\alpha,\beta)$ moving under the condition that the line $y = \alpha x + \beta$ is a tangent to the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$, is

Question

Dr. Abubacker · Accepted Answer

(a)
Given line $y = ax + \beta$ is a tangent to given hyperbola, if $\beta^{2} = a^{2}\alpha^{2} - b^{2}$
Hence, locus of $(\alpha,\beta)$ is $y^{2} = a^{2}x^{2} - b^{2}$, which represents a hyperbola

Q. The locus of a point $P(\alpha,\beta)$ moving under the condition that the line $y = \alpha x + \beta$ is a tangent to the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$, is

Explanation

Reviewed by Dr. Abubacker

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