Question

A circle whose parametric coordinates are given by $x=\frac{a}{\sqrt{2}}+a\cos \theta$ and $y=\frac{a}{\sqrt{2}}+a\sin \theta$, then choose correct option(s) among the following.

• A. will pass through origin
• B. will have the radius $\frac{a}{\sqrt{2}}$ units
• C. will pass through $(\frac{a}{\sqrt{2}},\frac{a}{\sqrt{2}})$
• D. will have the radius of $a$ units

Answer 1

Answer: (A), (D)

The correct options are
A will pass through origin
D will have the radius of $a$ units

Given $x=\frac{a}{\sqrt{2}}+a\cos \theta ,y=\frac{a}{\sqrt{2}}+a\sin \theta$
$\Rightarrow {(x-\frac{a}{\sqrt{2}})}^2=a^2{\cos }^2\theta ,{(y-\frac{a}{\sqrt{2}})}^2=a^2{\sin }^2\theta$
$\Rightarrow {(x-\frac{a}{\sqrt{2}})}^2+{(y-\frac{a}{\sqrt{2}})}^2=a^2\Rightarrow x^2+y^2-\sqrt{2}ax-\sqrt{2}ay=0$
Hence circle will pass through $(0,0)$ and have the radius of $a$ units.