JEE MainMathematicsEasyApplication of derivatives

If θ denotes the acute angle between the curves, y=10-x^2 and
y=2+x^2 at a point of their intersection, then |tanθ | is equal

Show answer and solution

y = x^{2} + 2\& y = 10 - x^{2}\

meet at

( \pm 2,6)

\frac{dy}{dx} = 2x\

for first curve and

\frac{dy}{dx} = - 2x\

for
second
hence slope are 4 and -4

\ so\ |tan\theta| = \left| \frac{4 - ( - 4)}{1 + 4( - 4)} \right| = \frac{8}{15}

Source: Grass-G / M-28 Mathematics Paper FST 16 Jan.docx

Need a video for this idea?

Scan any doubt from your notes and get a whiteboard explanation.