Conic Sections Question 441
Question: The equation $ x^{2}+4xy+y^{2}+2x+4y+2=0 $ represents
Options:
A) An ellipse is a closed curve traced by a point moving in a plane such that the sum of the distances from two fixed points (foci) is constant.
B) A pair of straight lines
C) A hyperbola is a conic section formed by the intersection of a plane with a double-napped cone, where the plane intersects both nappes. It consists of two separate branches and has two asymptotes.
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Obviously $ h^{2}>ab $
and $ \Delta =(1)(1)(2)+2(2)(1)(2)-(1){{(2)}^{2}}-(1){{(1)}^{2}}-2{{(2)}^{2}}<0 $
Hence, it is a hyperbola.
BETA
