**Standard form of a circle :**

** **In an x-y Cartesian coordinate system, the circle with center (a, b) and radius r is the set of all points (x, y) such that

(x - a)^{2} + (y - b)^{2} = r^{2}

This equation of the circle follows from the Pythagorean Theorem applied to any point on the circle: as shown in the diagram to the right, the radius is the hypotenuse of a right-angled triangle whose other sides are of length x − a and y − b. If the circle is centered at the origin (0, 0), then the equation simplifies to

x^{2} + y^{2} = r^{2}

Source - Wikipedia

1) Determine the standard form of circle equation with radius 9 and center (−5, 13).

**Solution:**

Given: r = 9 a = - 5 b = 13

The standard form of a circle is given by

** (x -
a) ^{2} + (y - b)^{2} = r^{2}**

(x - (-5))^{2} + (y -
13)^{2} = 9^{2}

(x + 5)^{2} + (y -
13)^{2} = 81

This is the required standard form of the circle equation.

2) Determine the standard form of circle equation with radius 13 and center ( -4, 17).

**Solution:**

Given: r = 13 a = - 4 b = 17

The standard form of a circle is given by

** (x -
a) ^{2} + (y - b)^{2} = r^{2}**

(x - (-4))^{2} + (y -
17)^{2} = 13^{2}

(x + 4)^{2}
+ (y - 17)^{2} = 169

This is the required standard form of the circle equation.

3) Determine the standard form of circle equation with radius 25 and center (−9, 20).

**Solution:**

Given: r = 25 a = - 9 b = 20

The standard form of a circle is given by

** (x -
a) ^{2} + (y - b)^{2} = r^{2}**

(x - (-9))^{2} + (y -
20)^{2} = 25^{2}

(x + 9)^{2} + (y -
20)^{2} = 625

This is the required standard form of the circle equation.

1) Determine the standard form of circle equation with radius 6 and center (−3, 10).

Answer: (x + 3)^{2} + (y - 10)^{2} = 36

2) Determine the standard form of circle equation with radius 11 and center (−7, 24).

Answer: (x + 7)^{2} + (y - 24)^{2} = 121