Question

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)

Answer #1

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.

Find an equation of a parabola satisfying the given conditions
Focus (4, 1) and directrix x = -2.

Write the equation for a parabola with a focus at (−3,−5) and a
directrix at x = −7

Find the vertex, focus and directrix of the following parabola
and sketch its graph
y+12x-2x^2=16

1.) Find the standard form of the equation of the parabola with
the given characteristic(s) and vertex at the origin.
Horizontal axis and passes through the point (−4, 7)
2.) Find the standard form of the equation of the parabola with
the given characteristics.
Vertex: (5, 1); focus: (3, 1)

1.find the equation of the ellipse with center (0,0), focus at
(4,0), vertices at (7,0) and major axis on the x-axis
2.A bridge is built in the form of a semi-elliptical arch. It
has an extension of 120 feet. The height of the arch that is 27
feet from its center is 9 feet. Find the height of the arch at its
center.

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.

Find the standard form of the equation of the parabola
satisfying the given conditions.
Vertex:
(1,−2);
Focus:
(1,−3)

1) Write the standard form of the equation of the parabola that
has the indicated vertex and whose graph passes through the given
point.
Vertex: (3, −1); point: (5, 7)
f(x) = __
2) Write the standard form of the equation of the parabola that
has the indicated vertex and whose graph passes through the given
point.
Vertex: (4, 5); point: (0, 1)
f(x) = __
3) Write the standard form of the equation of the parabola that
has the indicated...

. Find the second degree equation if the vertex of the parabola
is (4, -2) and one point on the parabola is (1, 5).
Sketch y = ?−4 /(?+1)(?−2)
Tell me ALL your considerations!
If there is a horizontal asymptote, does your graph cross it?
Where? Show me your work to justify your answer.

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