Conic Sections Question 441

Question: The equation $ x^{2}+4xy+y^{2}+2x+4y+2=0 $ represents

Options:

A) An ellipse

B) A pair of straight lines

C) A hyperbola

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.