Question

Plz help with equation of the circle will award fastest CORRECT answer with brainliest

Answer 1

Answer:

$(x-1)^2+(y-2)^2=6.25$

Step-by-step explanation:

The equation for a circle is given by:

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

Where (h,k) is the center and r is the radius.

The center is the red dot, which is (1,2). Thus, h=1 and k=2.

To find the radius, you need to use the distance formula. We are given two coordinates: the center (red dot) at (1,2) and a blue dot on the circle at (2.5,4). Find the radius by using the distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Let (1,2) be x₁ and y₁ and let (2.5,4) be x₂ and y₂. Therefore:

$d=\sqrt{(2.5-1)^2+(4-2)^2}\\d=\sqrt{(1.5)^2+2^2}\\d=\sqrt{2.25+4}\\d=\sqrt{6.25}=2.5$

Thus, r is 2.5.

Plugging these numbers into the equation, we have:

$(x-h)^2+(y-k)^2=r^2\\(x-1)^2+(y-2)^2=2.5^2\\(x-1)^2+(y-2)^2=6.25$