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? A. C, D, and E are unchanged. B. C increases, but D and E are unchanged. C. C and D decrease, but E is unchanged. D. C, D, and E increase. E. C and D are unchanged, but E decreases.

Answer 1

C and D are unchanged, but E decreases.

Explanation:

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Answer 2

The equation of a circle is x2 + y2 + Cx + Dy + E = 0

The radius of the circle is decreased without changing the coordinates of the centre point.

Now we know that general equation of a circle is x^2 + y^2 +2gx +2fy +c

Here C=2g and D =2f and we know that -g and -f are co-ordinates of centre point which remains unchanged

So here in the given problem C and D are unchanged .

But we know that radius of a circle = √(g^2 + f^2 -c)

Here c is E and we are given that radius is decreased which is only possible when value of c i.e. E gets increased.

So correct answer is value of C and D remains unchanged but value of E is increased.