Question

Write the equation of a circle centered at the

Answer 1

Answer:

$(x+4)^2+(y+6)^2=100$

Step-by-step explanation:

Given a circle centred at the point P(-4,-6) and passing through the point

R(2,2).

To find its equation, we follow these steps.

Step 1: Determine its radius, r using the distance formula

For point P(-4,-6) and R(2,2)

$\text{Distance Formula=}\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\text{Radius=}\sqrt{(2-(-4))^2+(2-(-6))^2} \\=\sqrt{(2+4))^2+(2+6)^2}\\=\sqrt{6^2+8^2}\\=\sqrt{100}\\Radius=10$

Step 2: Determine the equation

The general form of the equation of a circle passing through point (h,k) with a radius of r is given as: $(x-h)^2+(y-k)^2=r^2$

Centre,(h,k)=P(-4,-6)

r=10

Therefore, the equation of the circle is:

$(x-(-4))^2+(y-(-6))^2=10^2\\\\(x+4)^2+(y+6)^2=100$