Answer:
The circle has a radius of 7 units.
Step-by-step explanation:
Center of the circle is at origin i.e. [tex]P(0,0)[/tex] 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 [tex]Q(0,7)[/tex] 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:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Here, the two points are P(0,0) and Q(0,7)
[tex]x_1 = 0\\y_1 = 0\\x_2 = 0\\y_2 = 7\\[/tex]
Putting the values and finding out radius:
[tex]Radius = \sqrt{(0-0)^2+(7-0)^2}\\\Rightarrow Radius = \sqrt{7^2}\\\Rightarrow Radius = 7\ units[/tex]
Hence, the correct option is Circle has a radius equal to 7.
