How do you write the standard form of the hyperbola #-x^2+y^2-18x-14y-132=0#?

Answer 1

Standard form of the hyperbola equation :
#(y-7)^2/100-(x+9)^2/100=1#.

The standard form of a hyperbola with centre, #(alpha,beta)# is #rarr#
#(y-beta)^2/b-(x-alpha)^2/a=1#
Therefore, the given expression can be arranged as #rarr#
#-(x^2+18x+81)+(y^2-14y+49)=(132-81+49)#
#:.(x+9^2)-(y-7)^2=-100#
#:.((x+9)^2/-100)-((y-7)^2/-100)=1#
#:.(y-7)^2/100-(x+9)^2/100=1#. (Answer).

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Answer 2

To write the standard form of the hyperbola, first, group the x-terms together and the y-terms together. Then, complete the square for both x and y terms separately. After completing the square, rearrange the equation into the standard form, which is ( \frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1 ) or ( \frac{(y - k)^2}{a^2} - \frac{(x - h)^2}{b^2} = 1 ), depending on whether the hyperbola opens horizontally or vertically.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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