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 + 4 intersect the circle with radius 3 and center (0, 4)?

Step-by-step explanation:

Recall that the equation for a circle is given by:

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

Then for a center of (0, 4) and a radius of 3, our equation is:

We want to know at what point does the circle intersect with the line:

Therefore, we can solve for x. To do so, substitute the linear equation into the circle equation:

Simplify:

Square:

Divide both sides by 5:

Therefore:

In QI, x is always positive, so we only need to consider the positive case:

Using the linear equation again, we can see that:

Therefore, the point in which a circle with center (0, 4) and a radius of 3 intersects the line with equation y = 2x + 4 in the first quadrant is the point:

Or approximately:

And we are finished!

step-by-step explanation:

x-intercept:

(

−

1

+

√

7

,

0

)

,

(

−

1

−

√

7

,

0

)

y-intercept:

(

0

,

−

6

)