Question

Let a curve $y=f\left(x\right),f\left(x\right)\ge 0\forall x\in R$ has property that for every point P on the curve, the length of subnormal is equal to abscissa of P. If f(1) = 3, then f(4) is equal to

• A. $-2\sqrt{6}$
• B. $2\sqrt{6}$
• C. $3\sqrt{5}$
• D. 6

Answer 1

The correct option is B $2\sqrt{6}$

$y\frac{dy}{dx}=x\Rightarrow y^2=x^2+cf\left(x\right)=\sqrt{x^2+8}\Rightarrow f\left(4\right)=2\sqrt{6}$