Question

What is an equation of a circle with center (2, -1) that passes through the point (3, 4)?

Answer 1

(x-2)²+(y+1)²=26

Explanation:

(x-2)²+(y+1)²=26

distance formula for radius

√(3-2)²+(4--1)² = √26

(x-h)²+(y-k)²=r²

Answer 2

(x - 2)^2 + (y + 1)^2 = 26

Explanation:

A circle with center O(2, -1) that passes through the point A(3, 4).

=> The radius of this circle is OA which could be calculated by:

OA = sqrt[(3 - 2)^2 + (4 - (-1))^2] = sqrt[1^2 + 5^2] = sqrt[26]

The equation of a circle with center O(a, b) and radius r could be written as:

(x - a)^2 + (y - b)^2 = r^2

=> The equation of circle O above with center O(2, -1) and radius = sqrt(26) is shown as:

(x - 2)^2 + (y - (-1))^2 = (sqrt(26))^2

<=>(x - 2)^2 + (y + 1)^2 = 26

Hope this helps!