A) \[{{x}^{2}}+{{y}^{2}}-2xy-18x-10y=0\]
B) \[{{x}^{2}}-18x-10y-45=0\]
C) \[{{x}^{2}}+{{y}^{2}}-18x-10y-45=0\]
D) \[{{x}^{2}}+{{y}^{2}}-2xy-18x-10y-45=0\]
Correct Answer: D
Solution :
The equation of the parabola is \[{{(x-1)}^{2}}+{{(y+1)}^{2}}=\frac{{{(x+y+7)}^{2}}}{2}\] \[{{x}^{2}}+1-2x+{{y}^{2}}+1+2y=\frac{{{(x+y+7)}^{2}}}{2}\] \[2{{x}^{2}}+2-4x+2{{y}^{2}}+2+4y={{(x+y+7)}^{2}}\]\[2{{x}^{2}}+4-4x+4y+2{{y}^{2}}\] \[={{x}^{2}}+{{y}^{2}}+14x+14y+2xy+49\] \[{{x}^{2}}+{{y}^{2}}-2xy-18x-10y-45=0\]
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