Question

Let $A(a\cos \theta ,0),B(0,a\sin \theta )$ be any two points then the distance between two points is

• A. $|a|units$
• B. $a^{2}units$
• C. $\sqrt{a}units$
• D. $\sqrt{2}aunits$

Answer 1

The correct option is A $|a|units$

As we know that distance $\left(d\right)$ between the two points $(x_1,y_1)$ is given as-

$d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

Therefore,

Distance between the points $(a\cos \theta ,0)$ and $(0,a\sin \theta )$-

$d=\sqrt{{(0-a\cos \theta )}^2+{(a\sin \theta -0)}^2}$

$\Rightarrow d=\sqrt{a^2{\cos }^2\theta +a^2{\sin }^2\theta }$

$\Rightarrow d=\sqrt{a^2({\cos }^2\theta +{\sin }^2\theta )}$

$\Rightarrow d=\sqrt{a^2}=\left|a\right|\text{units}$