Question

What is the length of the radius and the coordinates of the center of the circle defined by the equation `(x+7)^2+(y-3)^2=121`?

Answer 1

The radius is `11 (14-3)` and the coordinates of the centre is (`7,3`)

Explanation:

Opening up the equation,
`(x+7)^2 + (y-3)^2 = 121`
`x^2+14x+49+y^2-6y+9 = 121`
`y^2-6y = 63-x^2+14x`

Find the x-intercepts, and the midpoint to find x-line of symmetry,
When `y = 0`,
`x^2-14x-63 = 0`
`x=17.58300524 or x=-3.58300524`

`(17.58300524-3.58300524)/2 = 7`

Find the highest and lowest point and midpoint,
When `x =7`,
`y^2-6y-112=0`
`y = 14 or y = -8`

`(14-8)/2 = 3`

Hence, the radius is `11 (14-3)` and the coordinates of the centre is (`7,3`)