Question

18. In the diagram below, PQRS is a square Find the equation of the circle that will pass through the four vertices of the square
R(2, - 2)

S

P(- 2, 2)

Q

Answer 1

An equation of the circle that will pass through the four (4) vertices of the square is (x + 2)² + y² = 2².

How to find the equation of this circle?

Mathematically, the general form of the equation of a circle is given by;

(x - h)² + (y - k)² = r²

Where:

• h and k represents the coordinates at the center.

• r is the radius of a circle.

Note: The center of a circle lies on the midpoint of the diagonal of a square, which is formed by joining its endpoints (opposite).

Midpoint on x-coordinate is given by:

Midpoint = (-2 - 2)/2

Midpoint = -4/2 = -2.

Midpoint on y-coordinate is given by:

Midpoint = (-2 + 2)/2

Midpoint = 0/2 = 0.

Thus, the center (h, k) = (-2, 0).

For the radius, we have:

r = √(-2)² + 0²

r = √4 = 2.

Substituting the parameters into the general equation, we have;

(x - (-2))² + (y - 0)² = 2²

(x + 2)² + y² = 2²

Read more on circle here: brainly.com/question/1615837

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