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If the asymptotes of the hyperbola $\left(x^{2} / a^{2}\right)-\left(y^{2} / b^{2}\right)=1$ intersect at right angles, then $a=b$ .

True

Calculus 2 / BC

Chapter 10

Conics, Parametric Equations, and Polar Coordinates

Section 1

Conics and Calculus

Polar Coordinates

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Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

Given the hyperbola $\frac…

02:45

Perpendicular Asymptotes F…

01:47

This set of exercises will…

07:14

Show that the lines $ y = …

01:53

SynthesisShow that a h…

a. Prove that the hyperbol…

02:43

An equation of a hyperbola…

05:05

00:56

Show that the asymptotes o…

04:17

Okay. What we want to do is to determine if this statement is true or false. So if, um ass and hopes, um, of hyperbole, um, which are given by X squared over a squared minus y squared over B squared equals toe one intersect at right angles, then a equals B. And that statement is true and is because is because if I actually look so typically when we grab a hyper Bella, we kind of use those values, um A and B to, um kind of doll in a box where the diagonals of the box will be our ask him tope. So our athlete hopes would be, oh, from the vertex of each of those boxes of that rectangle or box through the center of that hyperbole. And so those would be my ass and hopes. And so we know that rectangles for rectangles where age is no equal be the side Ling's um, the diagonals, um do not intersect at right angles. But what we do know from Geometry square, a square where a does equal be, um the diagonals do intersect at right angles. So the only thing that will get those enters at those ass and hopes to intersect at right angles because they are actually the diagonals of this box I make based on what A and B are the only one that, well, give me Internet intersection of right angles is a square where a has to equal be so I kind of defaulted on to some geometry.

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