Question

HURRY IM BEING TIMED !!!!!!!! The center of a circle is at the origin on a coordinate grid. A line with a positive slope intersects the circle at (0, 7). Which statement must be true? The circle has a radius greater than 7. The circle has a radius equal to 7. The slope of the line is equal to 7. The slope of the line is not equal to 7.

Answer 1

It's B

The circle has a radius equal to 7.

Explanation:

Just trust me

Answer 2

The circle has a radius of 7 units.

Explanation:

Center of the circle is at origin i.e.
`P(0,0)` Where P is the point where center of the circle lies.

A line with a positive slope, cuts the circle at point (0,7)

Let
`Q(0,7)` be the point where the line intersects the circle.

Please refer to the attached diagram for circle.

Clearly, it means that there is a point on circle which is at (0,7).

Radius of a circle is the distance between the center of circle and any point on circle.

We can use distance formula for finding the circle's radius:

`D = √((x_2-x_1)^2+(y_2-y_1)^2)`

Here, the two points are P(0,0) and Q(0,7)

`x_1 = 0\\y_1 = 0\\x_2 = 0\\y_2 = 7\\`

Putting the values and finding out radius:

`Radius = √((0-0)^2+(7-0)^2)\\\Rightarrow Radius = √(7^2)\\\Rightarrow Radius = 7\ units`

Hence, the correct option is Circle has a radius equal to 7.