Question

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

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

Answer 1

Answer: (D)

$(x-4)^2-16-4\left(y^2+4 y\right)=4$
$(x-4)^2-4\left[(y+2)^2-4\right]=20$
$(x-4)-4(y+2)^2=4 $
$\frac{(x-4)^2}{4}-\frac{(y+2)^2}{1}=1 \text { which is a hypererbola } $
$x-4=2 \sec \theta \Rightarrow x=4+2 \sec \theta \text { and } y+2=\tan \theta \Rightarrow y=-2+\tan \theta \Rightarrow (D)$