मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Choose correct alternatives: The combined equation of the coordinate axes is

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प्रश्न

Choose correct alternatives:

The combined equation of the coordinate axes is

पर्याय

  • x + y = 0

  • xy = k

  • xy = 0

  • x - y = k

MCQ
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उत्तर

The combined equation of the coordinate axes is xy = 0.

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Pair of Straight Lines - Miscellaneous Exercise 4 [पृष्ठ १३०]

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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 1.11 | पृष्ठ १३०

संबंधित प्रश्‍न

Find the combined equation of the following pair of line:

x + 2y - 1 = 0 and x - 3y + 2 = 0


Find the combined equation of the following pair of lines:

Passing through (2, 3) and perpendicular to the lines 3x + 2y – 1 = 0 and x – 3y + 2 = 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:

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

5x2 + 2xy - 3y2 = 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 


Choose correct alternatives:

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


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 = ______.


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 ______.


The area of triangle formed by the lines x2 + 4xy + y2 = 0 and x - y - 4 = 0 is ______.


Choose correct alternatives:

If distance between lines (x - 2y)2 + k(x - 2y) = 0 is 3 units, then k = ______.


Find the joint equation of the line:

x - y = 0 and x + y = 0


Find the joint equation of the line:

x + y − 3 = 0 and 2x + y − 1 = 0


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 (3, 2) and parallel to the lines x = 2 and y  = 3.


Find the joint equation of the line passing through the origin and perpendicular to the lines x + 2y = 19 and 3x + y = 18


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 joint equation of the pair of a line through the origin and perpendicular to the lines given by

x2 + 4xy - 5y2 = 0


Find the joint equation of the pair of a line through the origin and perpendicular to the lines given by

x2 + xy - y2 = 0


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 one of the lines given by 6x2 + kxy + y2 = 0 is 2x + y = 0.


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


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.


The combined equation of the two lines passing through the origin, each making angle 45° and 135° with the positive X-axis is ______  


Show that the combined equation of pair of lines passing through the origin is a homogeneous equation of degree 2 in x and y. Hence find the combined equation of the lines 2x + 3y = 0 and x − 2y = 0


The joint equation of pair of straight lines passing through origin and having slopes `(1 + sqrt2) and (1/(1 + sqrt2))` is ______.


The joint equation of pair of lines through the origin, each of which makes an angle of 60° with Y-axis, 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 ______.


Write the separate equations of lines represented by the equation 5x2 – 9y2 = 0


The line 5x + y – 1 = 0 coincides with one of the lines given by 5x2 + xy – kx – 2y + 2 = 0 then the value of k is ______.


Find the combined equation of the pair of lines passing through the origin and perpendicular to the lines represented by 3x2 + 2xy – y2 = 0.


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 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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