Recall the equation for a circle with center (h, k) and radius r. At what point in the first quadrant does the line with equation y=2x+5 intersect the circle with radius 5 and center (0, 5)?

(2.236,9.472).

Step-by-step explanation:

The standard form of a circle is

    ...(1)

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

It is given that radius of the circle is 5 and center at (0,5). So, the equation of circle is

    ...(2)

The given equation of line is

      ...(3)

We need to find the intersection point of line and circle in first quadrant.

On solving (2) and (3), we get

At x=2.236,

At x=-2.236,

It means line intersect the circle at (2.236,9.472) and (-2.236,0.528).

In first quadrant both coordinates are positive.

Therefore, the required point is (2.236,9.472).

r = 78539458390583095803458309458039485093485 or just 3

step-by-step explanation: