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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Choose correct alternatives: Auxiliary equation of 2x2 + 3xy - 9y2 = 0 is - Mathematics and Statistics

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प्रश्न

Choose correct alternatives:

Auxiliary equation of 2x2 + 3xy - 9y2 = 0 is

पर्याय

  • 2m2 + 3m - 9 = 0 

  • 9m2 - 3m - 2 = 0

  • 2m2 - 3m + 9 = 0

  • - 9m2 - 3m + 2 = 0

MCQ
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उत्तर

Auxiliary equation of 2x2 + 3xy - 9y2 = 0 is 9m2 - 3m - 2 = 0.

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Pair of Straight Lines - Miscellaneous Exercise 4 [पृष्ठ १२९]

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 4 Pair of Straight Lines
Miscellaneous Exercise 4 | Q 1.03 | पृष्ठ १२९

संबंधित प्रश्‍न

Find the combined equation of the following pair of lines:

2x + y = 0 and 3x − y = 0


Find the separate equation of the line represented by the following equation:

3y2 + 7xy = 0 


Find the separate equation of the line represented by the following equation:

x2 - 4xy = 0 


Find the separate equation of the line represented by the following equation:

`3"x"^2 - 2sqrt3"xy" - 3"y"^2 = 0`


Find the separate equation of the line represented by the following equation:

x2 + 2xy tan α - y2 = 0


Find the combined equation of the pair of a line passing through the origin and perpendicular to the line represented by the following equation:

xy + y2 = 0 


Find the combined equation of the pair of a line passing through the origin and perpendicular to the line represented by the following equation:

3x2 − 4xy = 0 


If the slope of one of the two lines given by `"x"^2/"a" + "2xy"/"h" + "y"^2/"b" = 0` is twice that of the other, then ab : h2 = ______.


The joint equation of the lines through the origin and perpendicular to the pair of lines 3x2 + 4xy – 5y2 = 0 is _______.


Choose correct alternatives:

If the equation 3x2 – 8xy + qy2 + 2x + 14y + p = 1 represents a pair of perpendicular lines, then the values of p and q are respectively ______.


Find the joint equation of the line passing through the origin and having inclinations 60° and 120°.


Find the joint equation of the line passing through (1, 2) and parallel to the coordinate axes


Find the joint equation of the line passing through (3, 2) and parallel to the lines x = 2 and y  = 3.


Find the joint equation of the line which are at a distance of 9 units from the Y-axis.


Find the joint equation of the line passing through (-1, 2) and perpendicular to the lines  x + 2y + 3 = 0 and 3x - 4y - 5 = 0


Show that the following equations represents a pair of line:

x2 + 2xy - y2 = 0


Show that the following equations represent a pair of line:

x2 - y2 = 0


Find the separate equation of the line represented by the following equation:

6x2 - 5xy - 6y2 = 0


Find the separate equation of the line represented by the following equation:

3x2 - y2 = 0


Find k, if the sum of the slopes of the lines given by 3x2 + kxy - y2 = 0 is zero.


Find k, if the sum of the slopes of the lines given by x2 + kxy − 3y2 = 0 is equal to their product.


Find k, if the slope of one of the lines given by 3x2 - 4xy + ky2 = 0 is 1.


Find k, if the slope of one of the lines given by 3x2 + 4xy + ky2 = 0 is three times the other.


Find the joint equation of the pair of lines through the origin and making an equilateral triangle with the line x = 3.


Find the combined equation of bisectors of angles between the lines represented by 5x2 + 6xy - y2 = 0.


Show that the following equation represents a pair of line. Find the acute angle between them:

2x2 + xy - y2 + x + 4y - 3 = 0


Show that the combined equation of the pair of lines passing through the origin and each making an angle α with the line x + y = 0 is x2 + 2(sec 2α)xy + y2 = 0


Find the condition that the equation ay2 + bxy + ex + dy = 0 may represent a pair of lines. 


If the line x + 2 = 0 coincides with one of the lines represented by the equation x2 + 2xy + 4y + k = 0, then prove that k = - 4. 


If equation ax2 - y2 + 2y + c = 1 represents a pair of perpendicular lines, then find a and c.


Find the joint equation of the line passing through the origin and having slopes 1 + `sqrt3` and 1 - `sqrt3`


The combined equation of the lines through origin and perpendicular to the pair of lines 3x2 + 4xy − 5y2 = 0 is ______


The joint equation of the lines through the origin which forms two of the sides of the equilateral triangle having x = 2 as the third side is ______


The equation of line passing through the midpoint of the line joining the points (-1, 3, -2) and (-5, 3, -6) and equally inclined to the axes is ______.


The joint equation of pair of lines having slopes `1+sqrt2` and `1-sqrt2` and passing through the origin is ______.


If `x^2/a + y^2/b + (2xy)/h` = 0 represents a pair of lines and slope of one line is twice the other, then find the value of ab : h2.


Find the joint equation of the pair of lines through the origin and perpendicular to the lines given by 2x2 + 7xy + 3y2 = 0


Find the combined equation of y-axis and the line through the origin having slope 3.


Find k, if one of the lines given by kx2 – 5xy – 3y2 = 0 is perpendicular to the line x – 2y + 3 = 0


The distance between the lines represented by the equation 4x² + 4xy + y² − 6x − 3y − 4 = 0 is


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