Question

If $9+f"\left(x\right)+f^{\prime }\left(x\right)=x^2+f^2\left(x\right)$ be the differential equation of a curve and let P be the point of minima then the number of tangents which can be drawn from P to the circle $x^2+y^2=9$ is

• A. 2
• B. 1
• C. either 1 or 2

Answer 1

The correct option is A 2

At the point of minima $f^{\prime }\left(x\right)=0,f"\left(x\right)>0$
$\Rightarrow f"\left(x\right)=-9+x^2+f^2\left(x\right)>0\Rightarrow x^2+y^2-9>0\Rightarrow$ point $P(x,f(x\left)\right)$ lies outside $x^2+y^2=9$
$\Rightarrow$ two tangents are possible.