2 years ago

Solve this system of equations using elimination. X-6=-17 -2x+12y=7

1 answer:

8 0

Answer:

Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.

Point Form:

(−11,−5/4)

Equation Form:

x=−11,y=−5/4

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Which is the equation of a hyperbola with directrices at x = ±3 and foci at (4, 0) and (−4, 0)?

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Answer:

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

Step-by-step explanation:

Since our foci are located on the x-axis, then our major axis is going to be the horizontal transverse axis of the hyperbola:

Formula for hyperbola with horizontal transverse axis centered at origin

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
Directrices -> $x=\pm\frac{a^2}{c}$
Foci -> $(\pm c,0)$ where $a^2+b^2=c^2$
$a>b$

Since we are given our directrices of $x=\pm3$ and foci of $(\pm4,0)$ , then we can set up the directrices equation to solve for $a^2$ :

$x=\pm\frac{a^2}{c}\\ \\\pm3=\pm\frac{a^2}{4}\\ \\12=a^2$

Now we can determine $b^2$ to complete our equation for the hyperbola:

$a^2+b^2=c^2\\\\12+b^2=4^2\\\\12+b^2=16\\\\b^2=4$

Therefore, our equation for our hyperbola is $\frac{x^2}{12}-\frac{y^2}{4}=1$

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