Maths-
General
Easy

Question

The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents an ellipse if

  1. triangle = 0, h2 < ab    
  2. triangle ≠ 0, h2 < ab    
  3. triangle≠ 0, h2 > ab    
  4. triangle ≠ 0, h2 = ab.    

hintHint:

The general equation of conics of a second degree is given by :
a x squared space plus space 2 h x y space plus space b y squared space plus space 2 g x space plus space 2 f y space plus space c space equals space 0 space
and discriminant triangle is given by :
a b c space plus space space 2 f g h minus space space a f squared space minus space b g squared space minus space c h squared

The correct answer is: triangle ≠ 0, h2 < ab


     The general equation of conics of a second degree is given by :
    a x squared space plus space 2 h x y space plus space b y squared space plus space 2 g x space plus space 2 f y space plus space c space equals space 0 space
    and discriminant triangle is given by :
    a b c space plus space space 2 f g h minus space space a f squared space minus space b g squared space minus space c h squared

    When :
    1 right parenthesis space triangle space equals space 0 comma space h squared less than space a b space minus space I t space r e p r e s e n t s space s t r a i g h t space l i n e s
2 right parenthesis space triangle space space not equal to space 0 comma space h squared space greater than space a b space minus space space I t space r e p r e s e n t s space h y p e r b o l a
3 right parenthesis space triangle space space not equal to space 0 comma space h 2 space equals space a b space minus space I t space r e p r e s e n t s space p a r a b o l a
4 right parenthesis space triangle space space not equal to space 0 comma space h 2 space less than space a b space minus space I t space r e p r e s e n t s space e l l i p s e

    Thus, The equation a x squared space plus space 2 h x y space plus space b y squared space plus space 2 g x space plus space 2 f y space plus space c space equals space 0 spacerepresents an ellipse if triangle space space not equal to space 0 comma space h 2 space less than space a b space.

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