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Algebra: Equation of Circle, Expansion and Difference Quotient

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1. The circle which has its center at the center of the hyperbola 4x2 +16x - 9y2 + 18y = 29 and whose diameter is the line segment between the vertices, what is the equation.
2. The coefficient of x7y9 in the expansion of (x-2) is?
3. Let f(x) = 2x + 1 , g(x) = x2 - 1 , and h(x) = square root (x + 1). Find the expansion for (f g h)(x).
4. Where f(x)= (2x+1)/ (4x+2), find and simplify the difference quotient [f( ½ +h) -f( ½ )] / h?

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1. First, we simplify the hyperbola . We can use the way of completing the squares. So we have

Thus the center of ...

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