Question

Use algebra to find each point at which the line (x-2y=-5) intersects the circle (x^2 + y^2 = 20)

Answer 1

I know the answer is (3,4) and (-5,0), but I have no idea how to get there.

Answer 2

\[x-2y=-5\]
\[x=2y-5\] replace in second equation get
\[(2y-5)^2+y^2=20\] solve this quadratic equation in y

Answer 3

some mistake in your answer or your question. i am going to guess that the circle should be
\[x^2+y^2=25\]am i right?

Answer 4

oh, you're right, it is x^2 + y^2 = 25, sorry!

Answer 5

because that would give you
\[(2y-5)^2+y^2=25\] and the solutions would be
\[y=0, y=4\] and in fact (3,4) is not on the circle you wrote

Answer 6

The back of my math book says the answer is (3,4),(-5,0)...so I'm not sure...

Answer 7

yeah that is fine

Answer 8

solve the quadratic equation
\[(2y-5)^2+y^2=25\] get
\[5y^2-20y+25=25\]
\[5y^2-20y=0\]
\[5y(y-4)=0\]
\[y=0, y =4\]

Answer 9

and then how do you find the x coordinate? do you plug it back in to the line equation?

Answer 10

replace y by 0 in the line, get x = -5,
replace y by 4 in the line, get x = 3

Answer 11

right, back in to the line equation

Answer 12

thank you so much!

Answer 13

yw