Question

The line $y=x+5$ touches

• A. the parabola $y^2=20 x$
• B. the ellipse $9 x^2+16 y^2=144$
• C. the hyperbola $\frac{x^2}{29}-\frac{y^2}{4}=1$
• D. the circle $x^2+y^2=25$

Answer 1

Answer: (A), (B), (C)

(A)$y^2=20 x=4(5) x$
$ \therefore$ Tangent : $y=m x+\frac{a}{m}$ for $m=1, a=5$
$\therefore y=x+5$ is a tangent to $y^2=20 x$
(B) $9 x^2+16 y^2=144 c^2=a^2 m^2+b^2 y=x+5 \Rightarrow m=1 ; c=5$
$\Rightarrow \frac{x^2}{16}+\frac{y^2}{9}=1: 5^2=16(1)^2+9 \Rightarrow$ True
$\therefore y=x+5$ is a tangent to $9 x^2+16 y^2=144$
(C) $c^2=a^2 m^2-b^2$
$\frac{x^2}{29}-\frac{y^2}{4}=1 \rightarrow a^2=29 ; b^2=4$
$5^2=29(1)^2-4 \rightarrow$ True $: y=x+5$ is a tangent
(D)
$\therefore y=x+5$ is NOT tangent to $x^2+y^2=25$