# Thread: Orthoganal Projectories

1. ## Orthoganal Projectories

Hello, I've recently encountered this problem: Prove these two equations are Orthoganal. x^2 + y^2 = r^2 | ax + by = 0 |

I get stuck after I differentiate both sides.

The left equation I get

2x + 2yy'= 0

= y' = -x/y

And the then the rightside

A + By' = 0

= y' = -a/b

I know I need to get rid of the A & B, but at the moment it's not clear to me. Any idea's on where to start? Thank you.

2. Originally Posted by Impalord
Hello, I've recently encountered this problem: Prove these two equations are Orthoganal. x^2 + y^2 = r^2 | ax + by = 0 |

I get stuck after I differentiate both sides.

The left equation I get

2x + 2yy'= 0

= y' = -x/y

And the then the rightside

A + By' = 0

= y' = -a/b

I know I need to get rid of the A & B, but at the moment it's not clear to me. Any idea's on where to start? Thank you.
Divide the equation ax + by = 0 by bx to see that a/b = –y/x.

3. Also note that $\displaystyle x^2+ y^2= r^2$ is the equation of a circle with center at the origin while Ax+ By= 0 is the equation of a straight line through the origin. In other words, for all A, B, and r, the line is a diameter of the circle.