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

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

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

Find the condition that the equation ay² + bxy + ex + dy = 0 may represent a pair of lines. 

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.

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. 

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.

If equation ax² - y² + 2y + c = 1 represents a pair of perpendicular lines, then find a and c.

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