Answer:
The point in the first quadrant is (3.33, 7.995).
Explanation:
The equation for a circle with center (h, k) and radius r is:

In this case, the center of the circle is (0, 3) and the radius is 6.
So the equation of the circle is:

We can rewrite this equation as:



The line with equation y = 1.5x + 3 intersects the circle when the two equations are equal.
So we can substitute y = 1.5x + 3 into the equation for the circle to get:

Expand the square term:

Distribute the constant term 6 on the right side of the equation:

Combine like terms:


Divide both sides by 3.25:

Take the square root of both sides:


Since we're looking for the point in the first quadrant, take the positive square root:

Now substitute the x value back into the line equation to find the corresponding y value:



So, the point of intersection between the line(y = 1.5x + 3 and the circle with center (0, 3)and radius 6 in the first quadrant is approximately (3.33, 7.995).