Question

If $m$ is the slope of a common tangent to the curves $\frac{x^{2}}{16}+\frac{y^{2}}{9}=1$

• A. 6
• B. 9
• C. 10
• D. 12

Answer 1

Answer: (B)

$\frac{ x ^{2}}{16}+\frac{ y ^{2}}{9}=1$
equation of tangent to the ellipse is
$y=m x \pm \sqrt{a^{2} m^{2}+b^{2}}$
$y=m x \pm \sqrt{16 m^{2}+9}$ ...(i)
$x^{2}+y^{2}=12$
equation of tangent to the circle is
$y = mx \pm \sqrt{12} \sqrt{1+ m ^{2}}$ ...(ii)
for common tangent equate eq. (i) and (ii)
$\Rightarrow 16\, m ^{2}+9=12\left(1+ m ^{2}\right)$
$16\, m ^{2}-12\, m ^{2}=3$
$4\, m ^{2}=3$
$12\, m ^{2}=9$