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Homework Statement
http://img103.imageshack.us/img103/3784/arch3tf0.jpg
[/URL]Homework Equations
On picture above
The Attempt at a Solution
Again, I just want someone to check my work.
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Conic sections are geometric shapes that are formed when a plane intersects a double cone at different angles. The four types of conic sections are circles, ellipses, parabolas, and hyperbolas.
Conic sections can be represented in equations using the general form Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, where the coefficients A, B, and C determine the type of conic section and the constants D, E, and F determine the position and size of the conic section.
The focus-directrix property is a characteristic of conic sections where the distance from any point on the conic section to a fixed point (called the focus) is equal to the distance from that point to a fixed line (called the directrix).
A conic section can have 0, 1, 2, 3, or 4 solutions, depending on the type of conic section and the values of its coefficients. For example, a circle can have 0 solutions if the radius is 0, but it can have 2 solutions if the radius is greater than 0.
Conic sections are used in many real-life applications, such as designing satellite orbits, creating parabolic mirrors for telescopes and headlights, and constructing bridges and arches. They are also used in physics and engineering to model the trajectories of objects and to optimize designs.