Question

What will be the equation of an ellipse translated vertically by $3$ units on the positive y - axis?

• A. $\frac{x^2}{a^2}+\frac{(y+3{)}^2}{b^2}=1$
• B. $\frac{(x-3{)}^2}{a^2}+\frac{(y-3{)}^2}{b^2}=1$
• C. $\frac{(x-3{)}^2}{a^2}+\frac{y^2}{b^2}=1$
• D. $\frac{x^2}{a^2}+\frac{(y-3{)}^2}{b^2}=1$

Answer 1

The correct option is D $\frac{x^2}{a^2}+\frac{(y-3{)}^2}{b^2}=1$

The standard equation of an ellipse is given by $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$.


The equation of an ellipse upon translating vertically by $k$ units changes to $\frac{x^2}{a^2}+\frac{(y-k{)}^2}{b^2}=1$.



On translating it vertically by $3$ units, the equation becomes
$\frac{x^2}{a^2}+\frac{(y-3{)}^2}{b^2}=1$