Help on Ellipse Example 5.4L - Understand m1 & m2

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The discussion focuses on Example 5.4L, specifically the determination of m1 and m2, which represent the points of intersection of two perpendicular tangents to an ellipse. The process begins by establishing the equation for a tangent line with an arbitrary slope m. To find the intersection of the two tangents, the condition of perpendicularity is applied, leading to the solution of the equations that yield the points m1 and m2.

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I need help with example 5.4L. I can understand all the working steps but i don't understand how they get m1 and m2, which is the point of intersection of the two perpendicular tangent... Can anyone enlighten me?
 
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Michael_Light said:
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I need help with example 5.4L. I can understand all the working steps but i don't understand how they get m1 and m2, which is the point of intersection of the two perpendicular tangent... Can anyone enlighten me?

First they determine what the equation is for a tangent for any given slope m.

Since they want to find the intersection of two tangents that are perpendicular to each other, they start with two tangents that have arbitrary slopes m1 and m2.

Then they introduce the condition that they are perpendicular.

And they solve the equations to find to point of intersection.
 

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