Find the center of the circle: x2 + 2x - 3 + y2 = 5.

Step-by-step explanation:

x² + 2x - 3 + y²  = 5

Strategy:

Convert the equation to the centre-radius form:

(x - h)² + (y - k)² = r²

The centre of the circle is at (h, k) and the radius is r .

Solution:

Move the number to the right-hand side.

x² + 2x + y²  = 8

Complete the square for x

(Take half the coefficient of x, square it, and add to each side of the equation)

(x² + 2x + 1) + y² = 9

Complete the square for y

The coefficient of y is zero.

(x² + 2x + 1) + y² = 9

Express the result as the sum of squares

(x + 1)² + y² = 3²

h = -1; k = 0; r = 3

The centre of the circle is at

The graph of the circle below has its centre at (-1,0) and radius 3.

in geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. by extension, a line and a plane, or two planes, in three-dimensional euclidean space that do not share a point are said to be parallel.