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

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10-2. Parabola, Ellipse, Hyperbola

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

A

Parabola

B

Ellipse

C

Hyperbola

D

Circle

Solution

$\frac{x^{2}}{1 / 4}-\frac{y^{2}}{1 / 3}=2$

$\therefore k^{2}=\frac{1}{4} \quad h^{2}-\frac{1}{3}$

$\Rightarrow \frac{\mathrm{h}^{2}}{4}-\mathrm{k}^{2}=\frac{1}{3} \quad \therefore$ a hyperbola

Standard 11

Mathematics

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