# Problems on Parabola, Ellipse and Hyperbola

#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

https://brainmass.com/math/graphs-and-functions/problems-parabola-ellipse-hyperbola-178829

#### Solution Preview

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.

...

#### Solution Summary

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