We present the solutions to the exercises in Tutorial on Equation of Circle with explanations.
Matched Exercise 1Find the equation of a circle whose center is at (2 , - 4) and radius 3.Solution to Matched Exercise 1(x - 2)^{2} + (y + 4)^{2} = 9
Matched Exercise 2Find the equation of a circle that has a diameter with the endpoints given by A(0 , -2) and B(0 , 2).Solution to Matched Exercise 2center at (0 , 0) radius = 2 equation: x^{2} + y^{2} = 4
Matched Exercise 3Find the center and radius of the circle with equationx^{2} - 2x + y^{2} - 8y + 1 = 0 Solution to Matched Exercise 3write the given equation in standard form by completing the squares. (x - 1)^{2} + (y - 4)^{2} = 4^{2} radius = 4 center at (1 , 4).
Matched Exercise 4Is the point P(-1, -3) inside, outside or on the circle with equation(x - 1)^{2} + ( y + 3)^{2} = 4 Matched Exercise 4center is at (1 , -3) and radius is equal to 2. distance d from center to the point (-1 , -3) is given by d = sqrt[(-1 - 1)^{2} + (-3 + 3)^{2}] = 2 Distance d is equal to the radius of the circle. Point P is on the circle. |