[Math] Application of derivative – finding the distance between line and origin

Question

Find the distance between the origin and the normal to the curve $y =e^{2x}+x^2$ drawn at the point $x =0$

After solving , I got the equation of normal is : $x+2y=2$

Please guide further, thanks.

Answer 1

Hint:

Now use the formula of distance from a given point:

$|\dfrac{Ax+By+C}{ \sqrt{A^2+B^2}}|$ is the distance from a point $(x,y$) for a line $Ax_1+By_1+C=0$