Answer:
The statement is a TRUE statement.
Step-by-step explanation:
We know that the standard form of an ellipse is given as:
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]
where a and b are the x and y-intercepts respectively.
Also when the denominator i.e. a=b then,
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{a^2}=1\\\\\\x^2+y^2=a^2[/tex]
Hence, we get the general equation of a circle whose center is at the origin and radius is 'a' or 'b' units.
Hence, the statement:
If the equation of an ellipse is in standard form and the denominators are equal, then the ellipse is a circle is a TRUE statement.
