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Find the equations of the hyperbola satisfying the given conditions.Foci $(\pm 4,0)$, the latus rectum is of length 12

$\frac{x^2}{4} - \frac{y^2}{12}=1$

Precalculus

Chapter 11

Conic Sections

Section 4

Parabola

Introduction to Conic Sections

Piedmont College

Oregon State University

Harvey Mudd College

Utica College

Lectures

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In Exercises $5-12,$ find …

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Find an equation for the c…

this problem, you first see that the folk I which is plus minus full common zero lies on the X axis. Which means that the equation of the hyperbole is of the form X square by square minus Y squared by b squared equals to one. You know that the foca is that plus minus c comma zero, which means that C is equal to four. Also the length of the latest victim is nothing but to be squared by A. Which has given us, Which means that the square equals to 60 now to get. And let's use the relationship between C and D. C square equals two. S squared plus b squared C square 16 equals two E squared plus 60. So this is nothing but a square plus six a -16 equals to zero. This is a square plus 80 minus, doing -16 equals to zero. Since a eight plus eight minus two, a plus eight equals to zero. This comes as a -2 Into a plus eight equals to zero. Or we get S two or minus is now we know that he cannot be negative. So the value of is let's get B squared b squared six and two A. Which is well, now let's get the equation of the high popular by substituting in me. So the equation is x squared by a square, It is four minus Y squared B squared plus 12 equals two. What?

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