Question

Write the equation of the circle that satisfies the given condition:

1. center ( 3.14 , -1/2), the radius is square root of 17

Answer 1

If coordinates of the center of the circle are $(x_0, y_0)$ and radius of the circle is $R$ then equation of the circle is such:

$$(x - x_0)^2 + (y - y_0)^2 = R^2$$

In our case:

$$x_0 = 3.14$$ $$y_0 = -\frac{1}{2}$$ $$R = \sqrt{17}$$

Substituting this into circle equation we get:

$$(x - 3.14)^2 + \left(y - \left(-\frac{1}{2}\right)\right)^2 = \sqrt{17}^2$$

Simplifying:

$$(x - 3.14)^2 + \left(y + \frac{1}{2}\right)^2 = 17$$