Final answer:
To find the area of the circle in the first quadrant with tangents on the y-axis and the x-axis, we can use the formula A = πr², where r is the radius of the circle. In this case, the area of the circle is 36π square units.
Step-by-step explanation:
To find the area of the circle, we need to determine its radius. Since the circle has a tangent on the y-axis at y = 6, we know that the distance from the center of the circle to the y-axis is 6 units. Let's call this distance r.
Since the circle also has a tangent on the x-axis, the distance from the center of the circle to the x-axis is also r units.
The area of a circle is given by the formula A = πr². So, the area of this circle would be A = π(6)² = 36π square units.
Learn more about Area of a circle