How do you decide whether or not the equation below has a circle as its graph If it does, give the center and the radius. If it does not, describe the graph #25x^2 +25y^2- 30x+ 30y -18 =0#?
The eqn. represents a circle having centre
The General Second Degree Equation in
In the event, its Centre is
In our Example,
So, the eqn. represents a circle having centre #(15/25,-15/25), i.e.,
Yes it is an equation of a circle.
If this an equation of a circle then we should be able to manipulate it back into standard form of
I spot that the standard form is part of the process for completing the square. Lets investigate that.
Divide throughout by 25 to get rid of the coefficients for
Completing the squares
Thus the centre as at point 1
The radius is
Is the same as:
Thus it is a circle.