Question

If $y=x+c$ is a tangent to the curve $9x^2+16y^2=144$ then value of $c$ is:

• A. $5$
• B. $-5$
• C. $\pm 5$
• D. $2$

Answer 1

The correct option is C $\pm 5$

To find value of $c$
If $y=x+c$ is a tangent to the curve
$9x^2+16y^2=144$
$\frac{x^2}{16}+\frac{y^2}{9}=1$
If the line $y=mx+c$ touch the ellipse
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ , then
$c=\pm \sqrt{a^2{m}^2+b^2}$
Therefore ,
$c=\pm \sqrt{16+9}$
$c=\pm 5$
Hence, Option C