Question

Write the equation of each circle

Center (-1,0) and containing the point (2, -4)

A.(x + 1)2 + y2 = 25
B.x2 + (y2 +1)= 25

Answer 1

The equation of the circle is
`(x + 1)^2 + y^2 = 25`

Explanation:

Equation of a circle:

The equation of a circle of centre
`(x_c,y_c)` has the following format:

`(x - x_c)^2 + (y - y_c)^2 = r^2`

In which r is the radius.

Center (-1,0)

This means that
`x_c = -1, y_c = 0`. So

`(x - x_c)^2 + (y - y_c)^2 = r^2`

`(x - (-1))^2 + (y - 0)^2 = r^2`

`(x + 1)^2 + y^2 = r^2`

Finding the radius:

Distance between the radius and the centre and a point of the circle. In this case, point (2,-4). Using the formula for the distance between two points:

`r = √((2-(-1))^2+(-4-0)^2) = √(3^2 + 4^2) = √(25) = 5`

So, the equation of the circle is:

`(x + 1)^2 + y^2 = 5^2`

`(x + 1)^2 + y^2 = 25`