Conic Sections Question 345
Question: The equation $ y^{2}-x^{2}+2x-1=0 $ represents
[UPSEAT 2004]
Options:
A) A hyperbola
B) An ellipse
C) A pair of straight lines
D) A rectangular hyperbola
Show Answer
Answer:
Correct Answer: C
Solution:
Given equation is $ y^{2}-x^{2}+2x-1=0 $
Comparing the given equation with $ ax^{2}+2hxy+by^{2}+2gx+2fy+c=0 $
we get,
$ a=1 $ , $ h=0 $ , $ b=1 $ , $ g=1 $ , $ f=0 $ , $ c=-1 $
$ \therefore $ $ \Delta =abc+2fgh-af^{2}-bg^{2}-ch^{2} $
$ \Delta =1+0+0-1=0 $
Hence, the given equation represents two straight lines.
BETA
