Question

Give the equation of the circle centered at the origin and passing through the point(0,10)

Answer 1

Answer:

$x^{2} + y^{2} = 100$

Step-by-step explanation:

The equation of a circle has the following format:

$(x - x_{0})^{2} + (y - y_{0})^{2} = r^{2}$

In which r is the radius(half the diameter) and the centre is the point $(x_{0}, y_{0})$

Centered at the origin

This means that $x_{0} = 0, y_{0} = 0$

Passing through the point(0,10)

The radius is the distance of any point in which the circle passes to the centre.

Using the formula for the distance between two points.

$r = D = \sqrt{(0 - 0)^{2} + (10 - 0)^{2}} = 10$

So

$x^{2} + y^{2} = 10^{2}$

$x^{2} + y^{2} = 100$