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.

    Related Questions to study

    General
    Maths-

    On a new year day every student of a class sends a card to every other student. The postman delivers 600 cards. The number of students in the class are :

    On a new year day every student of a class sends a card to every other student. The postman delivers 600 cards. The number of students in the class are :

    Maths-General
    General
    Maths-

    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

    Maths-General
    General
    Maths-

    An ellipse has OB as a semi – minor axis, F, F' are its foci and the angle FBF' is a right angle. Then the eccentricity of the ellipse is

    An ellipse has OB as a semi – minor axis, F, F' are its foci and the angle FBF' is a right angle. Then the eccentricity of the ellipse is

    Maths-General
    parallel
    General
    General

    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

    GeneralGeneral
    General
    Maths-

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

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

    Maths-General
    General
    Maths-

    If S’ and S are the foci of the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1 and P (x, y) be a point on it, then the value of SP + S’P is

    If S’ and S are the foci of the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1 and P (x, y) be a point on it, then the value of SP + S’P is

    Maths-General
    parallel
    General
    Maths-

    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

    Maths-General
    General
    Maths-

    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

    Maths-General
    General
    Maths-

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

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

    Maths-General
    parallel
    General
    Maths-

    The sum of all possible numbers greater than 10,000 formed by using {1,3,5,7,9} is

    Here, some students randomly select the numbers and try to add them which is very lengthy as there are 120 numbers and can lead to mistakes. Also, some students do not consider the place value but in questions such as addition, subtraction, etc. of numbers, place value method is most promising.
     
     
     
     
     

    The sum of all possible numbers greater than 10,000 formed by using {1,3,5,7,9} is

    Maths-General

    Here, some students randomly select the numbers and try to add them which is very lengthy as there are 120 numbers and can lead to mistakes. Also, some students do not consider the place value but in questions such as addition, subtraction, etc. of numbers, place value method is most promising.
     
     
     
     
     

    General
    Maths-

    Number of different permutations of the word 'BANANA' is

    In this question, one might think that the total number of permutations for the word BANANA is 6!
    This is wrong because in the word BANANA we have the letter A repeated thrice and the letter N repeated twice.

    Number of different permutations of the word 'BANANA' is

    Maths-General

    In this question, one might think that the total number of permutations for the word BANANA is 6!
    This is wrong because in the word BANANA we have the letter A repeated thrice and the letter N repeated twice.

    General
    Maths-

    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

    Maths-General
    parallel
    General
    Maths-

    Four dice are rolled then the number of possible out comes is

    Four dice are rolled then the number of possible out comes is

    Maths-General
    General
    Maths-

    The number of ways in which 5 different coloured flowers be strung in the form of a garland is :

    The number of ways in which 5 different coloured flowers be strung in the form of a garland is :

    Maths-General
    General
    Maths-

    Number of ways to rearrange the letters of the word CHEESE is

    Number of ways to rearrange the letters of the word CHEESE is

    Maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.