Question

The equation of the circle with centre (8, 5) and radius 6 is :

• A. $$(x-8)^2+(y-5)^5=36$$
• B. $$x^2-y^2=36$$
• C. $$(x-5)^2+(y-8)^2=36$$
• D. $$(x-8)^2+(y-5)^5=6$$

Answer 1

Answer:

$$(x-8)^2+(y-5)^5=36$$

Equation of a Circle

Standard Form of a Circle Equation

The standard equation of a circle with center $(h, k)$ and radius $r$ is given by: $(x-h)^2 + (y-k)^2 = r^2$

Applying the Formula

• Given the center of the circle is $(8, 5)$. Therefore, $h=8$ and $k=5$.

• Given the radius of the circle is $6$. Therefore, $r=6$.

• Substitute these values into the standard equation:$(x-8)^2 + (y-5)^2 = 6^2$

Simplifying the Equation

• Calculate the square of the radius: $6^2 = 36$.

• The final equation of the circle is:$(x-8)^2 + (y-5)^2 = 36$