(A): Given equation of curve \(2 x^{2}+y^{2}-3 x+5 y-8=0\) Put origin is translated to the point \((-1,2)\) We know that the coordinate of transformed point \(\mathrm{x}=\mathrm{X}+\mathrm{h} \Rightarrow \mathrm{y}=\mathrm{Y}+\mathrm{K}\) \(\therefore \quad \mathrm{x}=\mathrm{X}-1 \Rightarrow \mathrm{y}=\mathrm{Y}+2\) \(\Rightarrow 2(\mathrm{x}-1)^{2}+(\mathrm{y}+2)^{2}-3(\mathrm{x}-1)+5(\mathrm{y}+2)-8=0\) \(\Rightarrow 2\left(\mathrm{x}^{2}+1-2 \mathrm{x}\right)+\mathrm{y}^{2}+4+4 \mathrm{y}-3 \mathrm{x}+3+5 \mathrm{y}+10-8=0\) \(\Rightarrow 2 \mathrm{x}^{2}+2-4 \mathrm{x}+\mathrm{y}^{2}+4+4 \mathrm{y}-3 \mathrm{x}+3+5 \mathrm{y}+2=0\) \(\Rightarrow 2 \mathrm{x}^{2}+\mathrm{y}^{2}-7 \mathrm{x}+9 \mathrm{y}+11=0\) \(\Rightarrow 2 \mathrm{x}^{2}+\mathrm{y}^{2}-7 \mathrm{x}+9 \mathrm{y}+11=0\) \(\Rightarrow 2 \mathrm{x}^{2}+\mathrm{y}^{2}-7 \mathrm{x}+9 \mathrm{y}+11=0\)
TS EAMCET-2021-04.08.2021
Co-Ordinate system
88230
If a variable line is moving such that the intercepts made by it on the coordinate axes are reciprocal to each other, then the points \(\mathbf{P}(\mathrm{x}, \mathbf{y})\) on such lines satisfy
1 \(x+y>4\)
2 \(4 x y>1\)
3 \(4 x y\lt 1\)
4 \(x+y=4\)
Explanation:
(C) : Equation of line is moving such that intercept mode by it on the coordinate axis and reciprocal to each other is \(a x+\frac{y}{a}=1 \Rightarrow a^{2} x-a+y=0\) \(\mathrm{a} \in \mathrm{R}\) \((1)^{2}-4 x y>0 \Rightarrow 4 x y\lt 1\)
(A): Given equation of curve \(2 x^{2}+y^{2}-3 x+5 y-8=0\) Put origin is translated to the point \((-1,2)\) We know that the coordinate of transformed point \(\mathrm{x}=\mathrm{X}+\mathrm{h} \Rightarrow \mathrm{y}=\mathrm{Y}+\mathrm{K}\) \(\therefore \quad \mathrm{x}=\mathrm{X}-1 \Rightarrow \mathrm{y}=\mathrm{Y}+2\) \(\Rightarrow 2(\mathrm{x}-1)^{2}+(\mathrm{y}+2)^{2}-3(\mathrm{x}-1)+5(\mathrm{y}+2)-8=0\) \(\Rightarrow 2\left(\mathrm{x}^{2}+1-2 \mathrm{x}\right)+\mathrm{y}^{2}+4+4 \mathrm{y}-3 \mathrm{x}+3+5 \mathrm{y}+10-8=0\) \(\Rightarrow 2 \mathrm{x}^{2}+2-4 \mathrm{x}+\mathrm{y}^{2}+4+4 \mathrm{y}-3 \mathrm{x}+3+5 \mathrm{y}+2=0\) \(\Rightarrow 2 \mathrm{x}^{2}+\mathrm{y}^{2}-7 \mathrm{x}+9 \mathrm{y}+11=0\) \(\Rightarrow 2 \mathrm{x}^{2}+\mathrm{y}^{2}-7 \mathrm{x}+9 \mathrm{y}+11=0\) \(\Rightarrow 2 \mathrm{x}^{2}+\mathrm{y}^{2}-7 \mathrm{x}+9 \mathrm{y}+11=0\)
TS EAMCET-2021-04.08.2021
Co-Ordinate system
88230
If a variable line is moving such that the intercepts made by it on the coordinate axes are reciprocal to each other, then the points \(\mathbf{P}(\mathrm{x}, \mathbf{y})\) on such lines satisfy
1 \(x+y>4\)
2 \(4 x y>1\)
3 \(4 x y\lt 1\)
4 \(x+y=4\)
Explanation:
(C) : Equation of line is moving such that intercept mode by it on the coordinate axis and reciprocal to each other is \(a x+\frac{y}{a}=1 \Rightarrow a^{2} x-a+y=0\) \(\mathrm{a} \in \mathrm{R}\) \((1)^{2}-4 x y>0 \Rightarrow 4 x y\lt 1\)