To which point the origin is to be shifted in order to eliminate first powers of \(x\) and \(y\) (\(x^1\)…
To which point the origin is to be shifted in order to eliminate first powers of \(x\) and \(y\) (\(x^1\) and \(y^1\) terms) from the equation \(4 x^2+9 y^2-8 x+36 y+4=0\) ?
\((1,2)\)
\((-1,2)\)
\((1,-2)\)
\((-1,-3)\)
Solution
Given equation is
\(\begin{aligned}
& & 4 x^2+9 y^2-8 x+36 y+4 & =0 \\
\Rightarrow & & 4(x-1)^2+9(y+2)^2 & =36 \\
\Rightarrow & & \frac{(x-1)^2}{9}+\frac{(y+2)^2}{4} & =1
\end{aligned}\)
If we shift the origin to \((l,-2)\), the equation reduce to \(\frac{x^2}{9}+\frac{y^2}{4}=1\) and it is free from \(x\) and \(y\) terms.