A) No locus if \[k>0\]
B) An ellipse, if \[k<0\]
C) A point if,\[k=0\]
D) A hyperbola, if \[k>0\]
Correct Answer: C
Solution :
Given equation, \[2{{x}^{2}}+3{{y}^{2}}-8x-18y+35-k=0\] Compare with \[a{{x}^{2}}+b{{y}^{2}}+2hxy+2gx+2fy+c=0\],we get \[a=2,\,\,\,b=3,\,\,\,h=0,\,\,\,g=-4,\,\,\,f=-9,\,\,\,c=35-k\] \[\Delta =abc+2fgh-a{{f}^{2}}-b{{g}^{2}}-c{{h}^{2}}\] \[=6(35-k)+0-162-48-0\] \[\Delta =210-6k-210=-6k\]; \[\Delta =0\], if \[k=0\] So, that given equation is a point if \[k=0\].
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