Help on Ellipse Example 5.4L - Understand m1 & m2

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In summary, the conversation is about finding the point of intersection of two perpendicular tangents in example 5.4L, with the speaker needing clarification on how the values of m1 and m2 are determined. The process involves determining the equations for the tangents, introducing the condition of perpendicularity, and solving for the intersection point.
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Michael_Light
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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.
 

Related to Help on Ellipse Example 5.4L - Understand m1 & m2

What is the purpose of "Help on Ellipse Example 5.4L - Understand m1 & m2"?

The purpose of this example is to help you understand how to calculate the properties of an ellipse, specifically the values for m1 and m2.

What is an ellipse?

An ellipse is a geometric shape that resembles a flattened circle. It has two focal points and all points on the ellipse are equidistant from these focal points.

What is m1 and m2 in the context of an ellipse?

m1 and m2 are the distances from the center of the ellipse to its two focal points. These values are used in the equation for calculating the properties of the ellipse.

How do I calculate m1 and m2?

To calculate m1 and m2, you need to know the length of the major axis (a) and the length of the minor axis (b) of the ellipse. Then, you can use the formula m1 = √(a² - b²) and m2 = -√(a² - b²).

What are some real-life examples of ellipses?

Ellipses can be found in many natural and man-made structures, such as planetary orbits, the shape of an egg, or the design of a satellite dish. They can also be seen in the shape of some fruits, such as apples and watermelons.

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