Write the equation for the circle with center at (1, - 2) and passing through the origin.

(x – 1)² + (y +2)² = 5

Step-by-step explanation:

recall that the general form of the equation for the circle is as follows:

(x – h)² + (y – k)² = r²

where, (h,k) are the coordinates for the center of the circle and r is the radius of the circle.

We are given that the center of the circle is at (1,-2). Comparing this with the description of h & k above, we can immediately conclude that h = 1 and k = -2.

Hence the only thing we are missing now is radius r.

It is given that the circle passes through the origin, hence if we draw a line between the origin (0,0) and the center (1,-2), this distance is the radius.

to find the distance between 2 points, we use the attached formula

Distance = radius, r = √ [ (1-0)² + (-2-0)²]

r = √ [ (1² + (-2)²]

r = √ [1 + 4] = √ 5

hence we can assemble the equation

(x – 1)² + (y – (-2))² = (√5)²

(x – 1)² + (y +2)² = 5

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