Question

ABCD is a square with side a(=9). Find the equation to the circle circumscribing the square if A is the origin

• A. x² + y² + a(x + y) = 0
• B. x² + y² = a(x - y)
• C. x² + y² = a(x + y)
• D. x² + y² + a(x - y) = 0

Answer 1

The correct option is C

x² + y² = a(x + y)

If we have the centre and radius of the circle ,we can write the equation of the circle .The centre of the circle will be the centre of the square ,because

it is equidistant from all the vertices. so the radius will be half of the diagonal.

$r=\frac{diagonal}{2}=\frac{\sqrt{2}a}{2}=\frac{a}{\sqrt{2}}$

$\Rightarrow x^2+y^2-ax-ay+\frac{a^2}{4}+\frac{a^2}{4}=\frac{a^2}{2}$

$\Rightarrow x^2+y^2=a(x+y)\Rightarrow c$

we can also solve this using general equation $x^2+y^2+2gx+2fy+c=0$ is the general equation of a circle .we know A,B,C and D are

the points on this circle .we can substitute the points in the equation of the circle to find the value g,f and c.