हिंदी

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

विकल्प

  • 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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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 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
अध्याय 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 combined equation of the following pair of line passing through (−1, 2), one is parallel to x + 3y − 1 = 0 and other is perpendicular to 2x − 3y − 1 = 0


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

5x2 – 9y2 = 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 following equation:

5x2 - 8xy + 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:

xy + y2 = 0 


Choose correct alternatives:

If two lines ax2 + 2hxy + by2 = 0 make angles α and β with X-axis, then tan (α + β) = _____.


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 _______.


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


Choose correct alternatives:

If h2 = ab, then slopes of lines ax2 + 2hxy + by2 = 0 are in the ratio


Choose correct alternatives:

If slope of one of the lines ax2 + 2hxy + by2 = 0 is 5 times the slope of the other, then 5h2 = ______


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 which are at a distance of 9 units from the Y-axis.


Find the joint equation of the line passing through the point (3, 2), one of which is parallel to the line x - 2y = 2, and other is perpendicular to the line y = 3.


Show that the following equations represents a pair of line:

4x2 + 4xy + 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:

x2 - 4y2 = 0


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

3x2 - y2 = 0


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

2x2 + 2xy - y2 = 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 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.


If the line 4x - 5y = 0 coincides with one of the lines given by ax2 + 2hxy + by2 = 0, then show that 25a + 40h + 16b = 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 following equation represents a pair of line. Find the acute angle between them:

(x - 3)2 + (x - 3)(y - 4) - 2(y - 4)2 = 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


If the lines given by ax2 + 2hxy + by2 = 0 form an equilateral triangle with the line lx + my = 1, show that (3a + b)(a + 3b) = 4h2.


Prove that the combined of the pair of lines passing through the origin and perpendicular to the lines ax2 + 2hxy + by2 = 0 is bx2 - 2hxy + ay2 = 0.


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


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 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 ______.


Write the joint equation of co-ordinate axes.


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


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