Question

The line $y=x+5$ touches

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