18. In the diagram below, PQRS is a square Find the equation of the circle that will pass through the four vertices of the squar
1 answer:
An equation of the circle that will pass through the four (4) vertices of the square is (x + 2)² + y² = 2².
<h3>How to find the equation of this circle?</h3>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.
<u>Note:</u> 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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