Question

The slope of the tangent to the curve $y=\sqrt{4-x^2}$ at the point where the ordinate and the abscissa are equal is

• A. -1
• B. 1
• C. 0
• D. none of these

Answer 1

The correct option is A -1

Given equation of curve is $y=\sqrt{4-x^2}$
$y^2=4-x^2$
$\Rightarrow \frac{dy}{dx}=-\frac{x}{y}$
Let $P(x_1,y_1)$ be the point on the curve such that $x_1=y_1$
So, slope of tangent to curve at P is $-1$.