Question

At what point the slope of the tangent to the curve $x^2+y^2-2x-3=0$ is zero

• A. $(3,0);(-1,0)$
• B. $(3,0);(1,2)$
• C. $(-1,0);(1,2)$
• D. $(1,2);(1,-2)$

Answer 1

The correct option is D $(1,2);(1,-2)$

$x^2+y^2-2x-3=0..\left(1\right)$
Differentiating w.r.t $x$
$2x+2y\frac{dy}{dx}-2=0\Rightarrow \frac{dy}{dx}=\frac{1-x}{y}$
For slope of tangent to be zero $\frac{dy}{dx}=0\Rightarrow x=1$
Substituting $x=1$ in (1). we get
$1+y^2-2-3=0\Rightarrow y=4\Rightarrow y=\pm 2$
Therefore, the points are $(1,2),(1-2)$
Hence, option 'D' is correct.