Functions Involving Parameters, Vectors, and Matrices

In each of the following Exercises 1 to 5, find the equation of the circle with

1. centre (0,2) and radius 2

In each of the following Exercises 1 to 5, find the equation of the circle with 2. center (–2,3) and radius 4

In each of the following Exercises 1 to 5, find the equation of the circle with

$\text{3.centre }\left(\frac{1}{2},\frac{1}{4}\right)\text{ and radius }\frac{1}{12}$

In each of the following Exercises 1 to 5, find the equation of the circle with

$\text{ 4. centre }(1,1)\text{ and radius }\sqrt{2}$

In each of the following Exercises 1 to 5, find the equation of the circle with $\text{5. centre }(-a,-b)\text{ and radius }\sqrt{a^{2}-b^{2}}$

In each of the following Exercises 6 to 9, find the center and radius of the circles.

6. $\left(x+5\right)^2+\left(y-3\right)^2=36$

In each of the following Exercises 6 to 9, find the center and radius of the circles. $x^{{ 2} }+y^{{ 2} }-4x-8y-45=0$

In each of the following Exercises 6 to 9, find the center and radius of the circles. $x^{{ 2} }+y^{{ 2} }-8x+10y-12=0$

In each of the following Exercises 6 to 9, find the center and radius of the circles. $2x^{2}+2y^{2}-x=0$

Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre is on the line 4x + y = 16.