To interpret:The given equation and decide if it represents a circle, a point or in the last case if it does not represent any graph.
The equation represents a point .
For a given circle with center and radius the equation is given as:
This is referred to as the Standard form for the equation of a given circle.
Moreover, if the center of the circle is nothing but the origin that is then the equation reduces to:
Completing Square method:
To apply this method on an equation of the form:
Method- Make sure that the coefficient of and then, add and subtract the square of the half of coefficient of and then club the terms using formulae:
Consider the given equation:
It can also be written as:
Now apply Completing Square Method on the two brackets:
Now shift the extra terms to the right hand side
Recall the identities:
Use this to get:
Now sum of two positive quantities can be only when each of them is individually equal to .
Therefore we get:
Thus,the equation represents a point .
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