Geometric Bites

Below are the workings you can use to find the intersection points of two quadratic equations . Part 1 Part 2   There is a free interactive graph related to these workings here: https://www.desmos.com/calculator/0twcp4hwx2

In this post I demonstrate how to find out where a line and circle intersect on a 2 dimensional plane. The first step is to write out the equations of a line and a circle. We then make sure for both equations 'y' is isolated . Once we have the equations for a line and a circle whereby 'y' is isolated, we can then go about finding the values of 'x' for where the line intersects the circle. Like so... After we have found the values of 'x' using the quadratic formula , we then plug them back in to y=mx+c to get the values of 'y' for which the line intersects the circle. And that's it basically. Below is a free interactive Desmos graph related to this work: https://www.desmos.com/calculator/w3tsnjajtx

Below are the workings required to build an interactive graph that finds the points where a line and quadratic equation intersect . Here 'a' is not equal to 0 as it becomes part of the denominator a fraction . Also, if 'a' were equal to 0, we'd have a line intersecting a line, not a parabola (for instance). When we have the formula for 'x', we just plug it back into the linear equation to get the outcomes for 'y'. And there we have it, the points where a line and quadratic equation intersect. To see the interactive graph I was talking about, visit the Desmos link below: https://www.desmos.com/calculator/sqzjajbhea