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

Answer: C and D will be unaffected while E will increase.

Explanation:

Since, Here equation of a circle is,
`x^2 + y^2 + Cx + Dy + E = 0`

But we know that the equation of the circle,

`x^2 + y^2 + 2hx +2ky + (h^2+k^2-r^2) = 0`

( By solving the equation of circle
`(x-h)^2+(y-k)^2=r^2` where (h,k) is the center of the circle and r is the radius of the circle )

By comparing given equation with the above general equation,

We get, C = 2h, D = 2k and E =
`(h^2+k^2-r^2)`

Since, If r decreases C will unaffected ( because C is free from r)

D will unaffected ( because D is also free from r)

But If r decreases E will increases. ( because E =
`(h^2+k^2-r^2)` )