Conic Sections Problems: Get Step-by-Step Solutions

To calculate: The vertices and foci of the conic section: $x 29 + y 24 = 1$

alesterp 2021-01-24

The polar equation of the conic with the given eccentricity and directrix and focus at origin: $r = 41 + \cos θ$

djeljenike 2021-01-24

The exercise provides the equation for a degenerate conical section. Fill in the square and describe the graph of each equation.
$4 x^{2} - y^{2} - 32 x - 4 y + 60 = 0$

usagirl007A 2021-01-15

To calculate: The equation $100 y^{2} + 4 x = x^{2} + 104$ in one of standard forms of the conic sections and identify the conic section.

sibuzwaW 2021-01-10

Word problem involving comic sections. A hall 100 feet in length is designed as a whispering gallery (See example 9 for Ellipses). If the focus is 25 feet from the center, how high will the ceiling be at the center?

jernplate8 2021-01-06

Write the equation of each conic section, given the following characteristics:
a) Write the equation of an ellipse with center at (3, 2) and horizontal major axis with length 8. The minor axis is 6 units long.
b) Write the equation of a hyperbola with vertices at (3, 3) and (-3, 3). The foci are located at (4, 3) and (-4, 3).
c) Write the equation of a parabola with vertex at (-2, 4) and focus at (-4, 4)

Dillard 2021-01-05

The type of the conic section using the Discriminant Test and plot the curve using a computer algebra system. $x^{2} - 2 x y + y^{2} + 24 x - 8 = 0$

Tazmin Horton 2020-12-31

The conclusion about the values of e for rlliptical equations. The provided equations of conic sections are,

A) $\frac{x^{2}}{36} - \frac{y^{2}}{13} = 1$

B) $\frac{x^{2}}{4} - \frac{y^{2}}{4} = 1$

C) $\frac{x^{2}}{25} - \frac{y^{2}}{16} = 1$

D) $\frac{x^{2}}{25} - \frac{y^{2}}{39} = 1$

E) $\frac{x^{2}}{17} - \frac{y^{2}}{81} = 1$

F) $\frac{x^{2}}{36} - \frac{y^{2}}{36} = 1$

G) $\frac{x^{2}}{16} - \frac{y^{2}}{65} = 1$

H) $\frac{x^{2}}{144} - \frac{y^{2}}{140} = 1$

Bergen 2020-12-28

For Exercise, an equation of a degenerate conic section is given. Complete the square and describe the graph of each equation.
$9 x^{2} + 4 y^{2} - 24 y + 36 = 0$

Anonym 2020-12-24

To determine: The conic section and to find the vertices and foci: $x^{2} - y^{2} y = 4$

Nann 2020-12-17

Use the Discriminant Test to determine the type of the conic section (in every case non degenerate equation). Plot the curve if you have a computer algebra system.
$2 x^{2} - 8 x y + 3 y^{2} - 4 = 0$

Carol Gates 2020-12-16

(a) Given the conic section $r = \frac{5}{7 + 3 \cos (θ)}$ , find the x and y intercept(s) and the focus(foci).
(b) Given the conic section $r = \frac{5}{2 + 5 \sin (θ)}$ , find the x and y intercept(s) and the focus(foci).

Ramsey 2020-12-05

Discover which type of conic section the following quadratic form represents and change it to principal axes. Express ${\vec{x}}^{T} = [x_{1} x_{2}]$ in terms of the new coordinate vector ${\vec{y}}^{T} = [y_{1} y_{2}]$
$x_{1}^{2} - 12 x_{1} x_{2} + x_{2}^{2} = 70$

EunoR 2020-11-27

We need to verify theorem 5 Focus-Directrix definition: $0 < e < 1 and c = d (e - 2 - 1)$

midtlinjeg 2020-11-24

Decide if the equation defines an ellipse, a hyperbola, a parabola, or no conic section at all.
$(a) 4 x^{2} - 9 y^{2} = 12 (b) - 4 x + 9 y^{2} = 0$
$(c) 4 y^{2} + 9 x^{2} = 12 (d) 4 x^{3} + 9 y^{3} = 12$

UkusakazaL 2020-11-23

To find: The equation of the given hyperbola. The foci of the hyperbola is $(0, \pm 5) and entricity is e - 1.5$ .

banganX 2020-11-22

The equation is $16 x^{2} + 9 y^{2} - 98 x + 5 y + 224 = 0$

glasskerfu 2020-11-11

Write the equation in standard form by filling in the square and indicate the conical section it represents.
$2 x^{2} + 2 y^{2} - 8 x - 8 y = 0$

illusiia 2020-11-11

If a conic section is written as a polar equation, and the denominator involves $\sin θ$ , what conclusion can be drawn about the directrix?

kuCAu 2020-11-10

Solve for the equation in standard form of the following conic sections and graph the curve on a Cartesian plane indicating important points.
1. An ellipse passing through (4, 3) and (6, 2)
2. A parabola with axis parallel to the x-axis and passing through (5, 4), (11, -2) and (21, -4)
3. The hyperbola given by $5 x^{2} - 4 y^{2} = 20 x + 24 y + 36 .$

When you are told to work with conic sections equations, think about how planets travel around the sun and how elliptical routes get in focus. Parabolic mirrors, solar explanations, and so on. We have conic sections practice problems with answers that will help you learn easier. In the majority of cases, one should start with conic section equations because it is where one must start. Alternatively, take your conic section equation and compare things to the answers that we have below. See provided conic sections examples as these solutions will provide you with great starting points.

Integral Calculus

Solve Conic Sections Problems with Expert Help