HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

Show that the following equations represent a pair of line:

x² + 7xy - 2y² = 0

Show that the following equations represent a pair of line:

`"x"^2 - 2sqrt3"xy" - "y"^2 = 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 the joint equation of the pair of a line through the origin and perpendicular to the lines given by

2x² - 3xy - 9y² = 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 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 one of the lines given by 3x² - kxy + 5y² = 0 is perpendicular to the line 5x + 3y = 0.

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

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

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.

Find a if the sum of the slopes of lines represented by ax² + 8xy + 5y² = 0 is twice their product.

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