Write the equation of a circle centered at the origin through point A (-2; 4)

First, we use the formula to find the distance between two points:

d = √ ((x2 – x1) ² + (y2 – y1) ²);

In this formula, the first point has coordinates (x1; y1) – (0; 0), the second – (x2; y2) – A (-2; 4).

We get:

d = √ ((- 2 – 0) ² + (4 – 0) ²) = √ (4 + 16) = √20.

Thus, the radius of the circle is √20.

Now we use the equation of the circle:

(x – x0) ² + (y – y0) ² = R²;

Where: x0 is the abscissa of the center of the circle; y0 is the ordinate of the center of the circle; R is the size of the radius of the circle.

By condition, the center of the circle is at the origin of the coordinate system, x0 = 0, y0 = 0, or O (0; 0). Previously found R = √20.

Substituting the data into the formula, we get:

(x – 0) ² + (y – 0) ² = (√20) ²;

x² + y² = 20 – this is the desired equation of the circle.