HyperbolaHardBloom L3

Question

The parametric equations for the conic section $x^{2} - 8x - 4y^{2} - 16y - 4 = 0$ are:

Options

A.$x = - 4 + 2sec\theta,y = 2 + tan\theta$
B.$x = 4 + 2tan\theta,y = - 2 + sec\theta$
C.$x = - 4 + 2tan\theta,y = 2 + sec\theta$
D.$x = 4 + 2sec\theta,y = - 2 + tan\theta$

Solution

Sol. 9. (d) $(x - 4)^{2} - 4(y + 2)^{2} = 4$

$$\frac{(x - 4)^{2}}{4} - (y + 2)^{2} = 1$$

$$(x,y) \equiv (4 + 2sec\theta, - 2 + tan\theta)$$

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