# A conic section is said to be circle if the eccentricity e=1

A conic section is said to be circle if the eccentricity e=1

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Explanation of conic section:
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Vasquez

Step 1

The eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape

Since the eccentricity of an ellipse $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$;

$$a \geq b$$ is given as

$$e=\sqrt{1-\frac{b^2}{a^2}}$$

A circle is an ellipse when a=b

so eccentricity of circle $$e=\sqrt{1-\frac{a^2}{a^2}}=\sqrt{1-1}=0$$