Q82 / 160 · AP EAMCET 2024 (21 May Shift 1) · Mathematics
When the origin is shifted to $(h, k)$ by translation of axes, the transformed equation of $x^2+2 x+2 y-7=0$ does not contain $x$ term and constant term. Then $(2 h+k)=$
- A$\frac{7}{2}$
- B$\frac{1}{2}$
- Correct answerC2
- D0
Solution
$\begin{aligned}
& \text { } \mathrm{X}+h=x, \mathrm{Y}+k=y \\
& (\mathrm{X}+h)^2+2(\mathrm{X}+h)+2(\mathrm{Y}+k)-7=0 \\
& \mathrm{X}^2+(2 h+2) \mathrm{X}+2 \mathrm{Y}+h^2+2 h+2 k-7=0
\end{aligned}$
To remove X - term, $2 h+2=0 \Rightarrow h=-1$ To remove constant term, $h^2+2 h+2 k-7=0$ $\Rightarrow 1-2+2 k-7=0 \Rightarrow k=4 \Rightarrow 2 h+k=-2+4=2$
To remove X - term, $2 h+2=0 \Rightarrow h=-1$ To remove constant term, $h^2+2 h+2 k-7=0$ $\Rightarrow 1-2+2 k-7=0 \Rightarrow k=4 \Rightarrow 2 h+k=-2+4=2$
Hence, the correct answer is option: 'C'.