smileycellist2
2021-08-15
Answered

Sketch the following conic sections:

${4}^{2}-4y+8-4{x}^{2}=0$

You can still ask an expert for help

odgovoreh

Answered 2021-08-16
Author has **107** answers

Step 1

Given Equation:${y}^{2}-4y+8-4{x}^{2}=0$

Converting the above equation in Standard hyperbola form standard form

$\frac{{(x-h)}^{2}}{{a}^{2}}-\frac{{(y-k)}^{2}}{{b}^{2}}=1$

The above equation in Standard form

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

comparing with the standard form we have$h=0,\text{}a=1,\text{}k=2,\text{}b=2$

Step 2

The graph of the above equation is shown below

Given Equation:

Converting the above equation in Standard hyperbola form standard form

The above equation in Standard form

comparing with the standard form we have

Step 2

The graph of the above equation is shown below

asked 2021-08-15

To determine: The radical form of

asked 2022-04-04

Equation of a section plane in hyperbolic paraboloid

Find the equation of a plane passing through Ox and intersecting a hyperbolic paraboloid$\frac{{x}^{2}}{p}-\frac{{y}^{2}}{q}=2z(p>0,q>0)$ along a hyperbola with equal semi-axes.

My attempt: The equation of a plane passing through Ox is$By+Cz=0$ . So $z=\frac{-By}{C}$ . Now substitute $z=\frac{-By}{C}$ into the equation of hyperbolic paraboloid $\frac{{x}^{2}}{p}-\frac{{y}^{2}}{q}=\frac{-2By}{C}$ and transform to $\frac{{x}^{2}}{p}-\frac{{(y-\frac{Bq}{C})}^{2}}{q}=-\frac{{B}^{2}q}{{C}^{2}}$ . What to do next? I don't understand how to find B and C if we assume $\frac{{x}^{2}}{p}-\frac{{(y-\frac{Bq}{C})}^{2}}{q}=-\frac{{B}^{2}q}{{C}^{2}}$ is a hyperbola with equal semi-axes.

Find the equation of a plane passing through Ox and intersecting a hyperbolic paraboloid

My attempt: The equation of a plane passing through Ox is

asked 2020-11-05

Solve, a.Determine the conic section of the polar equation $r=\frac{8}{2+2\mathrm{sin}\theta}$ represents. b. Describe the location of a directrix from the focus located at the pole.

asked 2022-02-10

How do you find the eccentricity, directrix, focus and classify the conic section $r=\frac{8}{4-1.6\mathrm{sin}\theta}$ ?

asked 2021-02-14

A conical surface (an empty ice-cream cone) with surface charge density ? has height h.Radius of the top is R.Find potential difference between vertex & center of the top.

asked 2022-03-19

I want to know how to find the vertices of the conic equation

20x^2 +4y^2-800=0

asked 2021-02-10

Identify the conic section given by ${y}^{2}+2y=4{x}^{2}+3$

Find its$\frac{\text{vertex}}{\text{vertices}}\text{}\text{and}\text{}\frac{\text{focus}}{\text{foci}}$

Find its