The locus of a point P(h, k) such that the li | vedclass

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(C) The equation of the hyperbola is $4x^2 - 3y^2 = 1$,which can be written as $\frac{x^2}{1/4} - \frac{y^2}{1/3} = 1$.The condition for the line $y =

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Hyperbola

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(C) The equation of the hyperbola is $4x^2 - 3y^2 = 1$,which can be written as $\frac{x^2}{1/4} - \frac{y^2}{1/3} = 1$.The condition for the line $y = mx + c$ to be a tangent to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ is $c^2 = a^2m^2 - b^2$.Here,$m = h$,$c = k$,$a^2 = \frac{1}{4}$,and $b^2 = \frac{1}{3}$.Substituting these values into the condition,we get $k^2 = \frac{1}{4}h^2 - \frac{1}{3}$.Rearranging the terms,we get $\frac{h^2}{4} - k^2 = \frac{1}{3}$,which represents a hyperbola.Replacing $(h, k)$ with $(x, y)$,the locus is $\frac{x^2}{4/3} - \frac{y^2}{1/3} = 1$,which is a hyperbola.

The locus of a point $P(h, k)$ such that the line $y = hx + k$ is tangent to the hyperbola $4x^2 - 3y^2 = 1$ is a/an

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