Question

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

EDGE2020 Option B :)

Explanation:

Answer 2

The correct option is 2. The circle has a radius equal to 7.

Explanation:

It is given that center of a circle is at the origin on a coordinate grid.

The standard form of the circle is

`(x-h)^2+(y-k)^2=r^2`

Where (h,k) is center of the circle and r is radius.

The equation of the circle is

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

`x^2+y^2=r^2`

The line intersects the circle at (0,7) it means the point lies on the circle.

Put x=0 and y=7 in the above equation.

`0^2+7^2=r^2`

`49=r^2`

`7=r`

Therefore the radius of the circle is 7 units.

The line is passing through the point (0,7) with positive slope. Two points are required to find the slope of a line.

Since we have a single point therefore we cannot find the slope of the line. Second option is correct.