Question

1) Write a polar equation of a conic with the focus at the origin and the given data: The curve is a hyperbola with eccentricity 7/4 and directrix y=6.

2a) Determine the equation of a conic that satisfies
the given conditions:

vertices: (-1,2), (7,2)

foci: (-2,2), (8,2)

b) Identify the conic: circle parabola, ellipse, hyperbola.

c) Sketch the conic.

d) If the conic is a hyperbola, determine the equations of the asymptotes.

Answer #1

Determine the equation of a conic that satisfies the
given conditions:
foci: (-1,2), (7,2)
vertices: (-2,2), (8,2)
b) Identify the conic: circle parabola, ellipse,
hyperbola.
c) Sketch the conic.
d) If the conic is a hyperbola, determine the
equations of the asymptotes.

Write a polar equation of a conic with the focus at the origin
and the given data. hyperbola, eccentricity 5/3, directrix y =
4

Find an equation for the ellipse that has its center at the
origin and satisfies the given conditions.
Vertices V(±6, 0), foci
F(±2, 0)
Find an equation for the ellipse that has its center at the
origin and satisfies the given conditions.
eccentricity
3
5
, vertices V(0, ±5)

1.
Determine the equation of the parabola with focus
(−3,5)
and directrix
y=1
2. Determine the equation of the parabola with focus
(5/2, −4)
and directrix
x=7/2
3. Determine the equation of the ellipse using the information
given.
Endpoints of major axis at
(4,0), (−4,0)
and foci located at
(2,0), (−2,0)
4. Determine the equation of the ellipse using the information
given.
Endpoints of major axis at
(0,5), (0,−5)
and foci located at
(3,0), (−3,0)

Rewrite the equation below so that it is in standard form. State
the type of conic section represented and identify all of the conic
section’s relevant characteristics (center, vertices, co-vertices,
foci, equations of asymptotes, directrix, and radius). Provide
exact answers. Then graph the conic section.
3?2- 2y2 -8 =12x- 4y

1. Write the equation for the following conic sections in
standard form:
(a) An ellipse centered at (2,-5) that passes through (2,-3)
with foci at (4,-5) and (0,-5).
(b) A hyperbola with vertices at (1,0) and (1, 4) and foci at
(1,-1) and (1, 5).

An equation of a hyperbola is given.
x2 − 3y2 + 48 = 0
a) Find the vertices, foci, and asymptotes of the hyperbola.
(Enter your asymptotes as a comma-separated list of equations.)
vertex
(x, y)
=
(smaller y-value)
vertex
(x, y)
=
(larger y-value)
focus
(x, y)
=
(smaller y-value)
focus
(x, y)
=
(larger y-value)
asymptotes
(
b) Determine the length of the transverse axis.
(c) Sketch a graph of the hyperbola.

An equation of a hyperbola is given.
x^2/ 9 - y^2//49=1
(a) Find the vertices, foci, and asymptotes of the hyperbola.
(Enter your asymptotes as a comma-separated list of equations.)
vertex
(x, y)
=
(smaller x-value)
vertex
(x, y)
=
(larger x-value)
focus
(x, y)
=
(smaller x-value)
focus
(x, y)
=
(larger x-value)
asymptotes
(b) Determine the length of the transverse axis.
(c) Sketch a graph of the hyperbola.

3) Find a polar equation of the conic in terms of r
with its focus at the pole. ( r=???)
a)(4, π/2) (parabola)
b) (4, 0), (12, π) (eclipse)
c) (8,pi/2), (16,3pi/2) (eclipse)

Write the standard polar equation for a hyperbola with one focus
at the pole and vertices at points (1, pi) and (30, pi).

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