Question

If the lengths of semi-major and semi-minor axes of an ellipse are 2 and $\sqrt{3}$ and their corresponding equations are y − 5 = 0 and x + 3 = 0, then write the equation of the ellipse.

Answer 1

$$\begin{gathered} \text{The lengths of the semi major and the semi minor axes of the ellipse are 2 and}\sqrt{3}\text{, respectively. Their corresponding equations are y-5=0 and x+3 =0.} \\ \mathrm{S}\text{o,}\mathit{\text{a}}\text{=2 and}\mathit{\text{b}}\text{=}\sqrt{3} \\ \mathrm{The}\mathrm{e}\text{quation of the ellipse is given by} \\ \frac{{\left(x+3\right)}^2}{4}+\frac{{\left(y-5\right)}^2}{3}=1 \\ \Rightarrow 3{\left(x+3\right)}^2+4{\left(y-5\right)}^2=12 \\ \Rightarrow 3\left(x^2+9+6x\right)+4\left(y^2+25-10y\right)=12 \\ \Rightarrow 3x^2+27+18x+4y^2+100-40y=12 \\ \Rightarrow 3x^2+4y^2+18x-40y+115=0 \end{gathered}$$