Home / Assignment Help / How many solutions does the equation −4x+9=−4x+9−4x+9=−4x+9 have?

How many solutions does the equation −4x+9=−4x+9−4x+9=−4x+9 have?

The general equation of a circle is  (x-a)^{2} + ( y-b)^{2} =  r^{2} where a and b are the x and y components of the center respectively. 

In order to get into this format, we have to use a method that I’m drawing a blank on the same, my apologies about that.

Anyway, what you want is to first isolate the variable on side so now you have:  x^{2} - 4x +  y^{2} - 8y = 5 (you’ll see why I rearranged this soon)

Now you have to make it into an equation that can be simplified into the format stated earlier.

So, You have to take the x & y terms (-4x & -8y in this case) divide them each by two, and then square them.

The result of this step is the equation:  x^{2} -4x + 4 +  y^{2} - 8y + 16 = 5 + 4 + 16 
Notice the new components that have been added (4 & 16) and how the have been added to both sides. That is an important step.

Now we simplify and get: (x-2)^{2} +  (y-4)^{2}  = 25

So the coordinate of the center is: (2,4) and the radius is 5

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