Question

Question #223a7

Answer 1

Equation of the circle `= x^2 + y^2 = 50`

Explanation:

Equation of circle with origin as center is
`x^2 + y^2 = a^2` where ais the radius of the circle.

To find the radius we have to calculate the distance from center to a point on the circumference.

`radjus r = sqrt( (0-(-7))^2 + (0-(-1))^2) = sqrt50`

Hence equation of the circle is `x^2 + y^2 = 50`

Verification by finding the distance from center to the other point on the circumference.

`radius r = sqrt( (0-5)^2 + (0-5)^2) = sqrt50`

Answer 2

`x^2+y^2=50`

Explanation:

You can find the solution by using the distance function. From either of the points to the centre. Since it is a circle, the distance from the edge to the centre is the radius.

`D=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`
`=sqrt((0--7)^2+(0--1)^2`
`=sqrt(49+1)`
`=sqrt(50)`

The radius is therefore `sqrt(50)`

Substituting this into the formula for a circle

`x^2+y^2=sqrt(50)^2`
`x^2+y^2=50`

Check this solution by substituting in point B

`5^2+5^2=50`
`50=50`