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SmartOwl94
Choose the equation for the hyperbola centered at the origin with the given characteristics. 1.one focus (0, square root of 34), one vertex (0, 5) 2.vertical transverse axis, b = 6, c = square root of 45 3.vertices (+-2, 0), perimeter of central rectangle 24 units
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The equation of a hyperbola that opens up/down (north/south) is \[ \frac{y^2}{a^2}- \frac{x^2}{b^2} =1 \] I remember that the y term goes first with "Y the smile? Y the frown?" For 1.one focus (0, square root of 34), one vertex (0, 5) we can plot these points |dw:1334667585835:dw| so we know we are looking for \[ \frac{y^2}{a^2}- \frac{x^2}{b^2} =1 \]
You should know that the vertex is "a" away from the center (0,0), so a=5 and a^2=25 we also need to know that the focus (call it c) is defined by \[c^2= a^2+b^2 \] They give us c= sqrt(34), so c^2 =34. we can now find b: 34= 25+b^2 b^2=9 and b=3 so the equation should be \[ \frac{y^2}{25}- \frac{x^2}{9} =1 \]