Prove that the product of two lines equations is hyperbola

kabutjv7
2022-04-30
Answered

Prove that the product of two lines equations is hyperbola

You can still ask an expert for help

girni67v

Answered 2022-05-01
Author has **12** answers

Step 1

Let

${L}_{1}=0$ and ${L}_{2}=0$

be two nonparallel lines then

${L}_{1}{L}_{2}=c$

means

${({L}_{1}+{L}_{2})}^{2}-{({L}_{1}-{L}_{2})}^{2}=4c$

which is the most general equation of a hyperbola.

Let

be two nonparallel lines then

means

which is the most general equation of a hyperbola.

asked 2021-02-15

a. What is the best way of determining whether the given equation is a circle?
b. How will you describe the graphs of the equations that are not circles?

asked 2021-02-08

Quadric Surfaces How are quadric surfaces and conic sections related?

asked 2021-01-31

How can you distinguish parabolas from other conic sections by looking at their equations?

asked 2021-08-13

The front (and back) of a greenhouse have the same shape and dimensions shown below. The greenhouse is 40 feet long and the angle at the top of the roof is

asked 2021-02-05

a) determine the type of conic
b) find the standard form of the equation
Parabolas: vertex, focus, directrix
Circles: Center, radius
Ellipses: center, vertices, co-vertices, foci
Hyperbolas: center, vertices, co-vertices, foci, asymptotes
$16{x}^{2}+64x-9{y}^{2}+18y-89=0$

asked 2021-08-10

Perform a rotation of axes to eliminate the xy-term. xy+5=0

asked 2020-10-18

Equations of Conic Sections Systems of Non-linear Equations
Solve eeach problem systematically
1. Find all values of m so that the graph $2m{x}^{2}\text{}-\text{}16mx\text{}+\text{}m{y}^{2}\text{}+\text{}7{y}^{2}=2{m}^{2}\text{}-\text{}18m$ is a circle.