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 = 0.5x + 5 intersect the circle with radius 3 and center (0,5)? X =
y =​

The point of intersection is:

Step-by-step explanation:

We want to find the point in QI at which the line with the equation:

Intersect a circle with a radius of 3 and a center of (0, 5).

First, write the equation of a circle. The equation for a circle is given by:

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

Since our center is (0, 5), h = 0 and k = 5. The radius is 3. So, r = 3. Substitute:

Simplify:

At the point where the two equations intersect, its x-coordinate and y-coordinate will be the same. Therefore, we can substitute the equation of the line into the equation of the circle and solve for x. So:

Simplify:

Square:

Combine like terms:

Solve for x:

Note that since we are looking for the point of intersection in QI, x should be positive. So, we can ignore the negative answer.

To find the y-coordinate, substitute the x-value back into either equation. Using the linear equation:

So, the point of intersection in QI is:

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