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# Ellipses, Hyperbolas and Parabolas : Vertices, Foci, Polar and Parametric Form

1.Determine the vertices and foci of the graph of x^2 y^2
---- - ---- = 1.
16 35
As an example.
Answer should look like (0, +-4/9) Veertices
(+-2sqrt13, 0) Foci

2. Rotate the axes to eliminate the xy-term.
8x^2+64xy+8y^2+12x+12y+9=0

3. Find the discriminate and classify the graph.
7x^2-9xy+4y^2-4x-4y=0

4. Find the polar form of the equation 6x^2+3xy+6y^2=(-3)

5. A soccer ball is kicked with an initial velocity of 48ft/sec at an angle of 49 dgrees to the horizontal. Which set of parametric equations describes the path of the ball?
a. x=48t sin49degrees; y=48t cos49degrees-16t^2
b. x=48t cos49degrees; y=48t sin49degrees-16t^2
c. x=48t cos49degrees-16t^2; y=48t sin49degrees
d. x=48t sin49degrees-16t^2; y=48t sin49degrees

6. Find the eccentricity of the ellipse: (y-5)^2
(x+6)^2 + ----------- = 1
64

#### Solution Preview

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1. Determine the vertices and foci of the graph of x^2 y^2
---- - ---- = 1.
16 35
As an example.
Answer should look like (0, +-4/9) Vertices
(+-2sqrt13, 0) Foci

From the equation, we get , , then . So we have: vertices; foci.

2. Rotate the axes to eliminate the ...

#### Solution Summary

Vertices, Foci, Polar and Parametric Form and Eccentricity are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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