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