Question

A particle moves along the curve $x^2+4=y$.The points on the curve at which the $y$ coordinates changes twice as fast as the $x$ coordinate, is

• A. $(1,5)$
• B. $(5,1)$
• C. $(1,2)$
• D. $(3,2)$

Answer 1

The correct option is A $(1,5)$

$x^2+4=y\Rightarrow 2xdx=dy$ but $dy=2dx$

So $2xdx=2dx$

$\Rightarrow 2x=2$

$\Rightarrow x=1$

$\Rightarrow y=1^2+4=5$