What is the radius of a circle whose equation is x² + y² - 10x + 6y + 18 = 0?

Solution:

The generalized form of the radius of the circle is written in the form below:

(x - h)² + (x - k)² = a² --------(1)

where (h, k) are the coordinates of the centre of the circle and a is the radius

Hence rewriting x² + y² - 10x + 6y + 18 = 0,

we get

x² - 10x + 25 + y² + 6y + 9

= -18 + 25 + 9

25 and 9 have been added to both sides of the equation.

Converting the above equation into the form depicted in equation (1) we get:

(x - 5)² + (y + 3)² = 16

(x - 5)² + (y + 3)² = 4²------ (2)

Equation (2) is therefore the equation of the circle centred at x = 5 and y = -3

i.e. (5, -3) and the radius is 4.

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What is the radius of a circle whose equation is x² + y² - 10x + 6y + 18 = 0?

Summary:

The radius of the given circle is 4.