HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

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:

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:

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 

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

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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 _______.

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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 ______.

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The combined equation of the coordinate axes is

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

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

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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 having slopes 2 and 3.

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.