The point (-5,2) lies on the circumference of a circle, centre (0, 0) - OCR - GCSE Maths - Question 19 - 2019 - Paper 6

To find the equation of the circle, we will use the standard form of the equation of a circle, which is given by:

$x^2 + y^2 = r^2$

Here,

• The center of the circle is at (0,0), so the equation simplifies to $x^2 + y^2 = r^2$.
• We need to find the radius, $r$, which is the distance from the center to the point (-5,2).

Using the distance formula:

$r = ext{Distance} = ext{sqrt}((x_2 - x_1)^2 + (y_2 - y_1)^2)$

Substituting the values:

$r = ext{sqrt}((-5 - 0)^2 + (2 - 0)^2) = ext{sqrt}(25 + 4) = ext{sqrt}(29)$

Therefore, the equation of the circle becomes:

$x^2 + y^2 = 29$