Quadratic Question (1 Viewer)

[RideTheLightnin]

Alright the question is as reads:

"Show that the line y=-x+3 cuts the circle x^2+y^2=25 in two points"

Alright so ive done the perpendicular distance formula, and got 3root2/2, so i know the line cuts through the circle, but how do i show where it crosses, or dont i do that?

And if you do, do i do it simultaneously or what?

Cheers.

 

[acmilan]

If it just says show it cuts at two points you dont need to find the actual points. But yes, if you want to find the points solve simultaneously.

 

[RideTheLightnin]

ok thanks for that.

but im not too sure on how you solve them simulatenously, as the x's are of different powers.

this is how i go
1) y=-x+3 and 2) x^2+y^2=25
and from here do i either square 1 or get the sqaure root of 2. I seem to get different answers.....

 

[rama_v]

ok thanks for that.

but im not too sure on how you solve them simulatenously, as the x's are of different powers.

this is how i go
1) y=-x+3 and 2) x^2+y^2=25
and from here do i either square 1 or get the sqaure root of 2. I seem to get different answers.....

y = -x + 3
y = 3-x
x² + y² = 25
x² + (3-x)² = 25
x² + (9 -6x + x²) = 25
Go from there... (simple quadratic equation)