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Show that the two asymptotes of the hyperbola $x^{2}-y^{2}=16$ are perpendicular to each other.

$m, m_{2}=-1$

Precalculus

Chapter 11

The Conic Sections

Section 5

The Hyperbola

Introduction to Conic Sections

An Introduction to Geometry

Campbell University

Piedmont College

University of Michigan - Ann Arbor

Lectures

07:16

In mathematics, a continuoâ€¦

04:09

00:56

Show that the asymptotes oâ€¦

01:11

Given the hyperbola $\fracâ€¦

02:45

Perpendicular Asymptotes Fâ€¦

07:14

Show that the lines $ y = â€¦

00:49

Find the equations of the â€¦

01:47

a. Prove that the hyperbolâ€¦

01:46

Find the equation of a hypâ€¦

01:54

05:34

02:37

Perpendicular Asymptotes <â€¦

we want to look at the happier Billa. It's squared minus y squared equals sits stain. And they asked us to show that the SM totes are perpendicular to each other. The first thing we want to do is put this in our standard Fulham. So we divide by sits tain Yeah, that's squared over sits stain minus y squared over six stain equals from one. Now our center is it 00 and discourages it stains for worse. So we can't four units to the right, before units to the left and then under the Westport there's a states takes we can't four units. Ah, and four units Dan, It wouldn't be drawn that about saying now the as some toads, Lau on top of the diagonals of that rectangle are actually the diagonals lounge, the s. And it's now way went four units, uh, and four units to the right Notice the Wyler subsidizing rose. So that s and towed is why equals 4/4 ads. And that's just like wills. It's now the other Assam tote You go four units up four units left and so that asked him to Would be Why equals now the slope is for Ah, and then for laughs or negative for work. And so this ask them. Tote is y equals negative. It's will the slow of, um, one of of that first sm tote is one, and the slope of the other Assen toad is negative ward. When when you have to slow jobs and you want to know if the lines are perpendicular, you find the product of their slopes. One tons negative born is negative. Woolen. When the product of the slopes is negative one, that means the lines are perpendicular, so the two slopes give a product of negative. Born first, those esteem toads are perpendicular.

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