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SynthesisShow that a hyperbola does not intersect its asymptotes. That is, solve the system of equations$$\begin{aligned}&\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\\&y=\frac{b}{a} x \quad\left(\text { or } y=-\frac{b}{a} x\right)\end{aligned}$$

There is no number $x$ such that $\frac{x^{2}}{a^{2}}-\frac{\left(\frac{b}{a} x\right)^{2}}{b^{2}}=1$,

Precalculus

Chapter 10

Analytic Geometry Topics

Section 4

Nonlinear Systems of Equations and Inequalities

Introduction to Conic Sections

Johns Hopkins University

Harvey Mudd College

Boston College

Utica College

Lectures

07:16

In mathematics, a continuo…

04:09

07:14

Show that the lines $ y = …

01:47

a. Prove that the hyperbol…

01:11

Given the hyperbola $\frac…

03:51

An equation of a hyperbola…

02:18

REVIEW The graph of $\left…

00:56

Show that the asymptotes o…

03:25

Graphing Shifted Hyperbola…

04:11

02:47

If the asymptotes of the h…

01:05

Graph each hyperbola and w…

in this caution were given with hyper bulla excess, spurred by a square minus y squared, divided by B squared equals 21 and it's a simple given by a bike was to be divided by a X notice, considered it as a question of move on and it as a question about two. So this substitute the question off a sim toward that is why it was Toby by a X in a questionable one. And we get X squared, divided by a squared miners, be by a X. The Holy Squared, divided by B squared, equals to one these employees X squared, divided by a square. Miners be square X squared, divided by a squared B squared equals to one. These employees excess squared, divided by a squared minus X squared or debated about a squared equals to one these employees zero equals to one, but zero can never be equal to one. That is not possible. And when we come across such condition, these tells us that there is no solution for this, and then we don't have any solution for a system off linear nonlinear equations. That means a seam thought and the hyper bola again neighbor intersect and spoon

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The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

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