Conic Sections Question 360
Question: The equation of $ 2x^{2}+3y^{2}-8x-18y+35=k $ represents
[IIT 1994]
Options:
A) No locus if $ k>0 $
B) An ellipse, if $ k<0 $
C) A point if, $ k=0 $
D) A hyperbola, if $ k>0 $
Show Answer
Answer:
Correct Answer: C
Solution:
Given equation, $ 2x^{2}+3y^{2}-8x-18y+35-k=0 $ Compare with $ ax^{2}+by^{2}+2hxy+2gx+2fy+c=0 $ ,we get $ a=2,b=3,h=0,g=-4,f=-9,c=35-k $
$ \Delta =abc+2fgh-af^{2}-bg^{2}-ch^{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 $ .
BETA
