Circles. WILL MEDAL AND FAN!!! At what point in the first quadrant does the line with equation y = 0.5 x + 2 intersect the circle with radius 3 and center (0, 2)?

Question

Circles.  WILL MEDAL AND FAN!!! At what point in the first quadrant does the line with equation y = 0.5 x + 2 intersect the circle with radius 3 and center (0, 2)?

hhopke · Answer

The homework is due in 6 minutes, by the way, so I need the crash course version. :)

hhopke · Answer

@Directrix @jim_thompson5910 @Nnesha ? You guys are all really good at math and online.

jim_thompson5910 · Answer

`circle with radius 3 and center (0, 2)` means we have the equation

(x-h)^2 + (y-k)^2 = r^2
(x-0)^2 + (y-2)^2 = 3^2
x^2 + (y-2)^2 = 9

hhopke · Answer

right.

jim_thompson5910 · Answer

replace the y with 0.5x+2, since y = 0.5x+2

x^2 + (y-2)^2 = 9
x^2 + (0.5x+2-2)^2 = 9
x^2 + (0.5x)^2 = 9
x^2 + 0.25x^2 = 9

I'll let you solve for x. Tell me what you get

hhopke · Answer

oooohhh...

hhopke · Answer

2.6832816

jim_thompson5910 · Answer

plus or minus that, but yes

hhopke · Answer

thanks!

jim_thompson5910 · Answer

then you use that x value to find the corresponding y value

jim_thompson5910 · Answer

oh wait, you're in the first quadrant

so nvm the negative part

hhopke · Answer

right. Thank you! :) (did it on a graphing calculator so I got the x and y value at the same time.)

jim_thompson5910 · Answer

ok great, you're welcome