Question

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?

Answer 1

While E will increase, C and D won't change.

What is coordinate geometry?

A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.

Due to the fact that the circle's equation is,

Nevertheless, we are aware of the circle's equation.

                           $x^{2}+y^{2}+C x+D y+E=0$

(By figuring out the circle's equation$(x-h)^{2}+(y-k)^{2}=r^{2}$, where r is the radius and (h,k) is the center)

                         $x^{2}+y^{2}+2 h x+2 k y+\left(h^{2}+k^{2}-r^{2}\right)=0$

The following equation is compared to the generic equation above.

Our results are C = 2h, D = 2k, and E $=\left(h^{2}+k^{2}-r^{2}\right)$

As a result, C will be unchanged if r lowers ( because C is free from r)

D won't be effected ( because D is also free from r)

E will, however, rise if r falls.

E$=\left(h^{2}+k^{2}-r^{2}\right)$

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