EllipseHardBloom L3
Question
Which of the following is an equation of the ellipse with centre $( - 2,1)$, major axis running from $( - 2,6)$ to $( - 2, - 4)$ and focus at $( - 2,5)$ ?
Options
A.$\frac{(x - 2)^{2}}{25} + \frac{(y + 1)^{2}}{16} = 1$
B.$\frac{(x + 2)^{2}}{25} + \frac{(y - 1)^{2}}{9} = 1$
C.$\frac{(x - 2)^{2}}{9} + \frac{(y + 1)^{2}}{25} = 1$
D.$\frac{(x + 2)^{2}}{9} + \frac{(y - 1)^{2}}{25} = 1$
Solution
Sol.(d) $\frac{(x + 2)^{2}}{a^{2}} + \frac{(y - 1)^{2}}{b^{2}} = 1$
$$\begin{matrix} & be = 4 = 5e \\ & \ \Rightarrow \ a^{2} = 5^{2} - (5e)^{2} = 25 - 16 = 9 \end{matrix}$$
Equation of ellipse is
$$\frac{(x + 2)^{2}}{9} + \frac{(y - 1)^{2}}{25} = 1$$
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