Answer:
The Point in the first quadrant is
.
Step-by-step explanation:
Since
we know the general equation of the circle whose center is at (h,k) and radius is r that is

we have given center is (0,3) and radius is r= 4
substituting in the general equation of the circle we get

Now substituting the y= 2.5x + 3 in the above equation we get


here subtracting 16 from both sides and also perform addition
we get

dividing both sides by 7.25 we get

taking square root both sides we get
![x= \frac{+}{-}\sqrt[2]{2.0268}](https://tex.z-dn.net/?f=x%3D%20%5Cfrac%7B%2B%7D%7B-%7D%5Csqrt%5B2%5D%7B2.0268%7D)
but we need positive value of x because both x and y are positive in the first quadrant
that is
![x= \sqrt[2]{2.0268}](https://tex.z-dn.net/?f=x%3D%20%5Csqrt%5B2%5D%7B2.0268%7D)
substituting this into the given equation of the line we get
y = 2.5(
)+3
y = 6.559
so the point in the first quadrant is (
,6.559)
that is required