Question

Find the equation of the circle that passes through the points $(1,0),(-1,0)$ and $(0,1)$.

• A. $x^2+y^2=1$
• B. $2x^2+y^2=1$
• C. $x^2+y^2=4$
• D. None of these

Answer 1

The correct option is A $x^2+y^2=1$

Let the required circle be $x^2+y^2+2gx+2fy+c=0$. .......(1)

It passes through $(1,0),(-1,0)$ and $(0,1)$. Therefore, on substituting the coordinates of three points successively in equation 1, we get,

$1+2g+c=0$ ....(2)

$1-2g+c=0$ ....(3)

$1+2f+c=0$ .....(4)

Subtracting 3 from 2, we get,

$4g=0⟹g=0$

Putting $g=0$ in 2 , we get, $c=-1$.

Now, putting $c=-1$ in 4, we get, $f=0$.

Substituting the values of $g,f$ and $c$ in equation 1, we obtain the equation of the required circle as $x^2+y^2=1$.