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General equation of second degree of the form ax^2+2hxy+by^2+2gx+2fy+c=o Steps involved in solving this please, with an example.

General equation of second degree of the form ax^2+2hxy+by^2+2gx+2fy+c=o


Steps involved in solving this please, with an example.

Grade:Upto college level

1 Answers

Amit Jain
askIITians Faculty 32 Points
8 years ago

In a second degree general equation, first the discriminant and determinant need to be examined.

if ? ≡ abc + 2fgh − af2 − bg2 − ch2 = 0 then the equation represents a pair of straight lines.

If not zero, then we examine the discriminant(D): (2h)^2-4ab = 4(h^2-ab)

  • If the D=0, then it represents a parabola.
  • if D<0 and h≠0 and a≠b, then it is an ellipse.
  • if D<0 and h=0 and a=b, then it is a circle.
  • if D>0 then it is a hyperbola. if a+b=0, then it is a rectangular hyperbola.

 

After analysing this, we proceed to the solutions accordingly.

 

 

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