To write the equation of a circle in standard form, we use the general equation:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle, and r is the radius.
Given that the circle passes through the point (0, √21/2) and the center of the circle is at the origin (0,0), we can find the radius using the distance formula:
r = √[(0 - 0)^2 + (√21/2 - 0)^2] = √(21/2)
Now we can substitute the values we know into the equation:
(x - 0)^2 + (y - 0)^2 = (√(21/2))^2
Simplifying, we get:
x^2 + y^2 = 21/2
To write this equation in standard form, we multiply both sides by 2 to eliminate the fraction:
2x^2 + 2y^2 = 21
So the equation of the circle in standard form is:
2x^2 + 2y^2 = 21