## Calculus 8th Edition

$y=\pm 2 (1+b^2)^{3/2}x^2+bx$
Write formula 11. $\kappa(x)=\dfrac{|f''(x)|}{[1+(f'(x))^2]^{3/2}}$ Let us consider $f(x)=ax^2+bx$ . This is the general equation of a parabola. Now, $f'(x)=2ax+b$ and $f''(x)=2a$ Thus,$\kappa(x)=\dfrac{|2a|}{[1+(2ax+b)^2]^{3/2}}$ or, $\kappa(0)=\dfrac{|2a|}{[1+b^2]^{3/2}}$[ $\kappa(0)$ is the curvature at origin.] or, $4=\dfrac{|2a|}{[1+b^2]^{3/2}}$ or, $a=\pm 2 (1+b^2)^{3/2}$ Therefore, the equation of parabola is $y=\pm 2 (1+b^2)^{3/2}x^2+bx$