Question

Which of the following is not the circle which passes through the origin and cut offs chords of length a from each of the lines $y=x$ and $y=-x$?

• A. $x^2+y^2-\sqrt{2}ax=0$
• B. $x^2+y^2+\sqrt{2}ax-\sqrt{2}ay=0$
• C. $x^2+y^2-\sqrt{2}ay=0$
• D. $Noneofthese$

Answer 1

The correct option is A $x^2+y^2-\sqrt{2}ax=0$

Equation of line

$y=x$ and $y=-x$

Let the centre of circle be $(h,k)$

The perpendicular distance of $(h,k)$

From these lines must be equal.

$\frac{h-k}{\sqrt{2}}$=$\frac{h+k}{\sqrt{2}}$

For this,

$k=0$, which means center is on x-axis $(h,0)$

The distance of $(h,0)$ from $y=x$ is $\frac{h}{\sqrt{2}}$

Using phythagoras theorem,

In the triangle formed by $y=x$ , $y=x$

and the perpendicular from $(h,0)$

Thus, centre is $(\frac{a}{\sqrt{2}},0)$ and the radius $=\frac{a}{\sqrt{2}}$.

Therefore, equation of circle is

${(x-\frac{a}{\sqrt{2}})}^2+y^2=\frac{a^2}{2}$

$x^2+y^2-\sqrt{2}ax=0$

Hence, this is the answer.