The equation of a circle is x2 + y2 + cx + dy + e = 0. if the radius of the circle is decreased without changing the coordinates of the center point, how are the coefficients c, d, and e affected?

There will be no change in C and D but E must increase.

Step-by-step explanation:

We are given a equation of circle as:

it could also be represented in general form of equation of circle as:

( since we add both the side of the equality by and   )

Hence, on comparing the equation with general form of the equation:

The center of circle is (g,h) and radius is r.

Here we have the center as:

and radius is given aS:

As there is no change in the center hence the value of and remains unchanged i.e. the value of C and D remains unchanged.

Now we are given that the radius of the circle is decreased.

that means the change in radius is due to the change in E.

Hence for the quantity to decrease E must increase so that the total quantity decreases.

Hence there will be no change in C and D but E must increase in order to decrease the radius of circle.

step-by-step explanation: