# How sketch complicated hyperbola?

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Can somebody please explain to me how make it into the general hyperbola form for any of those questions? Thanks a lot!

Can somebody please explain to me how make it into the general hyperbola form for any of those questions? Thanks a lot!

##### 1 Answer

#### Answer:

Please read Rotation of Axes

#### Explanation:

None your parabolas are going to fit the standard forms:

because they are rotated hyperbolas.

The only equation that they are going to fit is equation

For example, equation [1]:

can be made to fit (9.4.1) by multiplying both sides by

and then moving everything to the left side:

Please observe that equation [1.1] is equation (9.4.1) with

How to sketch the equation

- Please observe that denominator in equation [1] forces a divide by zero condition at
#x =1# . This means that the asymptotes are the lines#x = 1# and#y = 1# and the center of the hyperbola is the intersection of the asymptotes, the point#(1,1)# - Please observe that in equation [1] the numerator forces a
#y = 0# condition at the point#x =-3# . This gives you the point#(-3,0)# . - Because the hyperbola is rotated
#pi/4# the vertices will be on the line#y = x# ; they are the points#(-1,-1)# and#(3,3)#

Here is a graph of

Both of your remaining equations can be sketched in exactly the same way. Please give it a try and feel free to ask questions, if you have any.