A) A pair of straight lines
B) An ellipse
C) A hyperbola
D) A parabola
Correct Answer: C
Solution :
\[{{x}^{2}}-2x-4{{y}^{2}}+16y-40=0\] Þ \[({{x}^{2}}-2x)-4({{y}^{2}}-4y)-40=0\] Þ \[{{(x-1)}^{2}}-1-4[{{(y-2)}^{2}}-4]-40=0\] Þ \[{{(x-1)}^{2}}-4{{(y-2)}^{2}}=25\] Þ \[\frac{{{(x-1)}^{2}}}{25}-\frac{{{(y-2)}^{2}}}{25/4}=1\], which is a hyperbola.
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