HSC Science (General) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions

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.

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

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 represents a pair of line:

4x² + 4xy + y² = 0

Show that the following equations represent a pair of line:

x² - y² = 0

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.