A circle has centre (4, –5) and radius 6 Find the equation of the circle - AQA - A-Level Maths Pure - Question 1 - 2022 - Paper 2

The standard form of the equation of a circle with centre

a = (h, k) and radius r is given by:

$(x - h)^2 + (y - k)^2 = r^2$

Substituting the values from the question where the centre is (4, -5) and radius is 6, we have:

• Here, h = 4 and k = -5.
• The radius r = 6.

Thus, we can substitute these values into the formula:

$$(x - 4)^2 + (y + 5)^2 = 6^2$$

This simplifies to:

$$(x - 4)^2 + (y + 5)^2 = 36$$

Hence, the correct equation of the circle is:

$$(x - 4)^2 + (y + 5)^2 = 36$$