Question

Consider the parabola $y^2=20 x$, ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ and hyperbola $\frac{x^2}{29}-\frac{y^2}{4}=1$
The equation of common tangents to all of them, is

• A. $y= \pm(x-5)$
• B. $y= \pm(x+3)$
• C. $y= \pm(x+5)$
• D. $y= \pm(x+4)$

Answer 1

Answer: (C)

If $y = mx + c$ is a common tangent, so
$c =\frac{5}{ m }= \pm \sqrt{16 m ^2+9}= \pm \sqrt{29 m ^2-4} \Rightarrow m ^2=1 \Rightarrow m = \pm 1$
So, $y= \pm(x+5)$