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Problems on Parabola, Ellipse and Hyperbola

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#1. Find the equation of parabola describe. Find 2 points of latus rectum.Graph.
Focus(-5,0) Vertex(0,0)

#2 Find the equation of the parabola. Find 2 points that define latus rectum. Graph. Focus (0,1) Diectrix line y= -1

#3. Find the equation of ellipse.draw the graph.
Center (0,0) Focus(0,8) Vertex (0,-10)

#4. Find the equation of ellipse.draw the graph
Focus at (0,8) Vertices at (0,+- 10)

#5. Find all the complex root. Leave your answer in polar form with the argument in degrees.
The complex fourth root of -81i

#6.Find the equation of hyperbola.
Vertices at(-3,0) and (3,0) Asymptote the line y=3x

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Solution Summary

The expert examines parabola, ellipse and hyperbola. Neat, step-by-step solutions to all the six questions are provided. Graphs included.

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The parabola is of the form y^2 = 4ax
Focus is given by (a, 0) = (-5, 0)  a = -5
The parabola is y^2 = -20x
Equation of the LR is x = -a
The equation is x = 5
Two points on the LR can be taken as (5, 1) and (5, 4)

#2 Find the equation of the parabola. Find 2 points that define latus rectum. Graph. Focus (0,1) Diectrix line y= -1

The parabola is of the form x^2 = 4ay
Focus is at (0, a) = (0, 1)  a = 1
The equation of the parabola is x^2 = 4y
Two points on the LR can be taken as (2, -1) and (4, -1)

#3. Find the equation of ellipse.draw the graph.
...

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