# Math: Points of Secancy

**URL:** <https://forum.kirupa.com/t/math-points-of-secancy/176278>\
**Category:** random\
**Created:** [January 22, 2006, 11:37am UTC](https://forum.kirupa.com/t/math-points-of-secancy/176278 "2006-01-22T11:37:21Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![TheCanadian](https://avatars.discourse-cdn.com/v4/letter/t/67e7ee/32.png) [@TheCanadian](https://forum.kirupa.com/u/TheCanadian)\
**Post date:** [January 22, 2006, 11:37am UTC](https://forum.kirupa.com/t/math-points-of-secancy/176278/1 "2006-01-22T11:37:21Z")

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Math time :king:

I’m working on a few AS2.0 classes for basic coordinate geometry and quadratic functions but my math knowledge has now reached it’s limit.

Given the equation of a circle: (x - h)² + (y - k)² = r²  
and the equation of a line: y = mx + b  
and the quadratic equation: x = (-b ±√(b² - 4ac)) / 2a

I came up with a few equations for determining the points of secancy of a line on a circle:  
(1 + m²)x² + (-2h + 2mx)x + (h² + z² -r ²)

Then plug that into the quadratic equation and we have the x coordinate of both points.

To find the y coordinate of each point, I have this equation:  
y = ±√(r² - (x - h)²) + k  
Where x is one of the points found earlier. So far so good.

The last equation gives you two values since the square root of a number has two answers (a positive and negative one) which makes sense since on a circle there are two possible points for each x value. How do you determine which one is the right one use. I was thinking I could check to see if each point lies on the secant and determine which ones are the right values - is this the right way to go.

Thanks :sc: