Question

List 1 consists of equations of tangents. List 2 consists of equations of conics. Match the options of list 1 with list 2.

Answer 1

A) $y=mx+c$ is tangent to $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ when $c^2=a^2{m}^2+b^2$
$\Rightarrow y=mx+\sqrt{a^2{m}^2+b^2}$ is equation of tangent of ellipse
B) $y=mx+c$ is tangent of $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ when $c^2=a^2{m}^2-b^2$
$\Rightarrow y=mx+\sqrt{a^2{m}^2-b^2}$ is equation of tangent of hyperbola
C) $y=mx+c$ is tangent of $y^2=4\left(\frac{a}{b^2}\right)x$ when $c=\frac{\left(\frac{a}{b^2}\right)}{m}=\frac{a}{b^{2}m}$
$\Rightarrow y=mx+\frac{a}{b^{2}m}$ is equation of tangent of parabola
D) $y=mx+c$ is tangent of $x^2+y^2=a^2+b^2$ when $c^2=(a^2+b^2)$
$\Rightarrow y=mx+\sqrt{a^2+b^2}$ is equation of tangent of circle