Question

The point on the curve $x^2+y^2=a^2,y\ge 0$ at which the tangent is parallel to $x$ axis

• A. $\left(a,0\right)$
• B. $\left(-a,0\right)$
• C. $\left(\frac{a}{2},\frac{\sqrt{3}a}{2}\right)$
• D. $\left(0,a\right)$
• E. $\left(0,a^2\right)$

Answer 1

The correct option is D

$\left(0,a\right)$

Explanation of the correct option.

Compute the required point:

Given: $x^2+y^2=a^2$………………..$\left(1\right)$

Differentiate with respect to $x$,

$\Rightarrow$$\frac{d}{dx}{x}^2+\frac{d}{dx}{y}^2=\frac{d}{dx}{a}^2$

$\Rightarrow$ $2x+2y\frac{dy}{dx}=0$

Since $\frac{dy}{dx}=0$

$\Rightarrow$ $x=0$

Substitute the value of $x$ in equation $\left(1\right)$,

$\Rightarrow$ $y=a$

Therefore, the required point is $\left(0,a\right)$.

Hence, option $\left(d\right)$ is the correct option.