Question

Write the equation in standard form for the circle that has a diameter with endpoints (22,0) and (2,0)

Answer 1

Answer:

(x - 12)² + y² = 100

Step-by-step explanation:

The standard form of the equation of a circle is;

(x - a)² + (y - b)² = r²

where:

a and b are the coordinates of the centre of the circle

r is the radius

We are given the coordinates of the endpoints of the diameter as; (22,0) and (2,0)

Thus, the centre of the circle would be at the mid point of the endpoints of the diameter.

Coordinates of the centre is;

((22 + 2)/2), (0 +0)/2))

This is;

(12, 0)

So, a = 12 and b = 0

Now,to get the radius r, we will use the formula;

r = √[(x2 - x1)² + (y2 - y1)²]

Where;

(x1, y1) and (x2, y2) are 2 points namely (12,0) and (22, 0)

r = √[(12 - 22)² + (0 - 0)²]

r = √(-10)²

r = √100

r = 10

Thus,equation of the circle is;

(x - 12)² + (y - 0)² = 10²

(x - 12)² + y² = 100