Answered

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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?

Sagot :

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

Step-by-step explanation:

Since, Here equation of a circle is, [tex]x^2 + y^2 + Cx + Dy + E = 0[/tex]

But we know that the equation of the circle,

[tex]x^2 + y^2 + 2hx +2ky + (h^2+k^2-r^2) = 0[/tex]

( By solving the equation of circle[tex](x-h)^2+(y-k)^2=r^2[/tex] 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 =[tex](h^2+k^2-r^2)[/tex]

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 =[tex](h^2+k^2-r^2)[/tex] )



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