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

$△$ = 0, h² < ab
$△$ ≠ 0, h² < ab
$△$ ≠ 0, h² > ab
$△$ ≠ 0, h² = ab.

hint Hint:

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 $a x squared space plus space 2 h x y space plus space b y squared space plus space 2 g x space plus space 2 f y space plus space c space equals space 0 space$ represents 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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The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents an ellipse if

= 0, h2 < ab ≠ 0, h2 < ab ≠ 0, h2 > ab ≠ 0, h2 = ab.

The general equation of conics of a second degree is given by :and discriminant is given by :

The correct answer is: ≠ 0, h2 < ab

The general equation of conics of a second degree is given by :and discriminant is given by :When :Thus, The equation represents an ellipse if .

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

$△$ = 0, h² < ab
$△$ ≠ 0, h² < ab
$△$ ≠ 0, h² > ab
$△$ ≠ 0, h² = ab.

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

A tangent to the ellipse x² + 4y² = 4 meets the ellipse x² + 2y² = 6 at P and Q. The angle between the tangents at P and Q of the ellipse x² + 2y² = 6 is

A tangent to the ellipse x² + 4y² = 4 meets the ellipse x² + 2y² = 6 at P and Q. The angle between the tangents at P and Q of the ellipse x² + 2y² = 6 is

The equation of the tangents drawn at the ends of the major axis of the ellipse 9x² + 5y² – 30y = 0 is

The equation of the tangents drawn at the ends of the major axis of the ellipse 9x² + 5y² – 30y = 0 is

For the ellipse 3x² + 4y² – 6x + 8y – 5 = 0

For the ellipse 3x² + 4y² – 6x + 8y – 5 = 0

The eccentricity of the curve represented by the equation x² + 2y² – 2x + 3y + 2 = 0 is

The eccentricity of the curve represented by the equation x² + 2y² – 2x + 3y + 2 = 0 is

The foci of the ellipse 25 (x + 1)² + 9 (y + 2)² = 225 are

The foci of the ellipse 25 (x + 1)² + 9 (y + 2)² = 225 are

The eccentricity of the ellipse 9x² + 5y² – 30y = 0 is

The eccentricity of the ellipse 9x² + 5y² – 30y = 0 is

The number of one - one functions that can be defined from $A equals left curly bracket a comma b comma c comma d right curly bracket$ into $B equals left curly bracket 12 comma 34 right curly bracket$ is

The number of one - one functions that can be defined from $A equals left curly bracket a comma b comma c comma d right curly bracket$ into $B equals left curly bracket 12 comma 34 right curly bracket$ is