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Write the equation in standard form for the ellipse $x^2 + 7y^2 = 21$ .

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Convert equations of conic sections from general to standard form

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Q. Write the equation in standard form for the ellipse

x^2 + 7y^2 = 21

.

Identify Standard Form: To write the equation in standard form, we need to have the equation in the form $(\frac{x^2}{a^2}) + (\frac{y^2}{b^2}) = 1$ , where $a$ and $b$ are the lengths of the semi-major and semi-minor axes, respectively.
Divide by $21$ : Divide both sides of the equation $x^2 + 7y^2 = 21$ by $21$ to get the equation in standard form. $\newline$ $(x^2/21) + (7y^2/21) = 21/21$
Simplify Equation: Simplify the equation to get the standard form. $\frac{x^2}{21} + \frac{y^2}{3} = 1$

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