Determine whether the statement below is true or false.
Every equation of the form $x^{2}+y^{2}+a x+b y+c=0$ has a circle as its graph.

Choose the correct answer below.
True
False

Answer

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Answer

Final Answer: $\boxed{\text{False}}$

Steps

Step 1 ：The equation given is of the form of a general circle equation, which is $(x-h)^2 + (y-k)^2 = r^2$, where (h,k) is the center of the circle and r is the radius.

Step 2 ：However, the equation given can also represent an ellipse, parabola, or hyperbola depending on the values of a, b, and c.

Step 3 ：Therefore, we cannot say that every equation of the given form will always represent a circle.

Step 4 ：Final Answer: $\boxed{\text{False}}$

Determine whether the statement below is true or false.Every equation of the form $x^{2}+y^{2}+a x+b y+c=0$ has a circle as its graph. Choose the correct answer below.TrueFalse

Answer

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Determine whether the statement below is true or false.
Every equation of the form $x^{2}+y^{2}+a x+b y+c=0$ has a circle as its graph.

Choose the correct answer below.
True
False