SOLUTION: write the equation in standard form: xsquared+ysquared-6x-4y+13=36 sorry that i cant find a small 2 for the squared. i hope this makes sense. please help me figure this out. t

Question 47791: write the equation in standard form:
xsquared+ysquared-6x-4y+13=36
sorry that i cant find a small 2 for the squared. i hope this makes sense. please help me figure this out. thanks so much!
Found 2 solutions by pizza, stanbon:
Answer by pizza(14) (Show Source): You can put this solution on YOUR website!
The first thing that needs clarification is the term 'standard form'.
The equation happens to be in standard form already.
However, I deduce from the title, that by standard form, you want to rearrange the equation such that it is evidently a conic section. The standard form of a conic section is as follows:

This implies that you have to do some factorisation.
I assume you are familiar with completing the square.
If you are, then you will know that

And

Then putting this into the original equation, we have

which is in standard form.
Hooray!
When c = d = 1, we have an equation for a circle, otherwise it is an equation of an ellipse. Circles and ellipses are conic sections.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
x^2+y^2-6x-4y+13=36
Complete the square on the x terms and on the y terms separately to get:
x^2-6x+9 +y^2-4y+4 =36-13+9+4
(x-3)^2 + (y-2)^2 = 36
This is the equation for a circle with center
at (3,2) and radius of 6
Cheers,
Stan H.

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