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ankoles [38]
3 years ago
7

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

Mathematics
1 answer:
rosijanka [135]3 years ago
4 0

Answer:

\boxed{(-1, 0)}

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 \boxed{(-1,0)}

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

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