Write the equation of a circle passing through point A (1; 3), if it is known that the center
June 12, 2021 | education
| Write the equation of a circle passing through point A (1; 3), if it is known that the center of the circle lies on the abscissa axis, and the radius is 5. How many such circles exist?
We have a point belonging to the circle: A (1; 3).
The radius of the circle and the coordinates of the center of the circle are known – they have the form (x0; 0).
Let’s write the equation of the circle:
(x – x0) ^ 2 + (y – y0) ^ 2 = R ^ 2.
We substitute the values we know:
(1 – x0) ^ 2 + (3 – 0) ^ 2 = 25;
(1 – x0) ^ 2 + 9 = 25;
(1 – x0) ^ 2 = 16;
1) 1 – x0 = -4;
x0 = 5;
2) 1 – x0 = 4;
x0 = -3.
We got two circles, since we also have two pairs of coordinates for the center of the circle – (5; 0) and (-3; 0).
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