An ellipse has 6 and 2 as length of major and minor axes respectively. If the centre is at $(5,6)$ and the major axis is along $x-y+1=0$, then the ellipse is

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Aicharya · Accepted Answer

Given, $2 a=6$ $\Rightarrow a=3$ and $2 b=2 \Rightarrow b=1$

Equation of $B C: x+y+k=0$ ...(i) It passes through $(5,6)$. $\therefore \quad k=-11$ Equation becomes $x+y-11=0$ Equation of ellipse $\frac{\left(\frac{x+y-11}{\sqrt{1^2+1^2}}\right)^2}{3^2}+\frac{\left(\frac{x-y+1}{\sqrt{1^2+1^2}}\right)^2}{1^2}=1$ $\begin{aligned} & \Rightarrow \quad \frac{(x+y-11)^2}{18}+\frac{(x-y+1)^2}{2}=1 \\ & \Rightarrow \quad(x+y-11)^2+9(x-y+1)^2=18\end{aligned}$

An ellipse has 6 and 2 as length of major and minor axes respectively. If the centre is at $(5,6)$ and the…

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