Question

Select the correct coordinate values for a vertical ellipse translated by $(h,k)$.

Answer 1

The equation of a translated vertical ellipse is $\frac{(x-h{)}^2}{a^2}+\frac{(y-k{)}^2}{b^2}=1$ where $b>a$.

All the terms are similar to that of a standard ellipse except when it is translated by $(h,k)$, $h$ and $k$ are added to them.

Focus of standard ellipse: $(0,\pm be)$
Focus of translated ellipse: $(h,k\pm be)$

Vertices of standard ellipse: $(0,\pm b)$
Vertices of translated ellipse: $(h,k\pm b)$

Equation of directrices of standard ellipse: $y=\pm \frac{b}{e}$
Equation of directrices of translated ellipse: $y=k\pm \frac{b}{e}$

Co - vertices of standard ellipse: $(\pm a,0)$
Co - vertices of translated ellipse: $(h\pm a,k)$