HSC Arts कक्षा ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Find the combined equation of the straight lines whose separate equations are x − 2y − 3 = 0 and x + y + 5 = 0

Show that 4x² + 4xy + y² − 6x − 3y − 4 = 0 represents a pair of parallel lines

Show that 2x² + 3xy − 2y² + 3x + y + 1 = 0 represents a pair of perpendicular lines

Show that the equation 2x² − xy − 3y² − 6x + 19y − 20 = 0 represents a pair of intersecting lines. Show further that the angle between them is tan⁻¹(5)

Prove that the equation to the straight lines through the origin, each of which makes an angle α with the straight line y = x is x² – 2xy sec 2α + y² = 0

Find the equation of the pair of straight lines passing through the point (1, 3) and perpendicular to the lines 2x − 3y + 1 = 0 and 5x + y − 3 = 0

Find the separate equation of the following pair of straight lines
3x² + 2xy – y² = 0

Find the separate equation of the following pair of straight lines
6(x – 1)² + 5(x – 1)(y – 2) – 4(y – 3)² = 0

Find the separate equation of the following pair of straight lines
2x² – xy – 3y² – 6x + 19y – 20 = 0

The slope of one of the straight lines ax² + 2hxy + by² = 0 is twice that of the other, show that 8h² = 9ab

The slope of one of the straight lines ax² + 2hxy + by² = 0 is three times the other, show that 3h² = 4ab

A ∆OPQ is formed by the pair of straight lines x² – 4xy + y² = 0 and the line PQ. The equation of PQ is x + y – 2 = 0, Find the equation of the median of the triangle ∆ OPQ drawn from the origin O

Find p and q, if the following equation represents a pair of perpendicular lines
6x² + 5xy – py² + 7x + qy – 5 = 0

Find the value of k, if the following equation represents a pair of straight lines. Further, find whether these lines are parallel or intersecting, 12x² + 7xy − 12y² − x + 7y + k = 0

For what values of k does the equation 12x² + 2kxy + 2y² +11x – 5y + 2 = 0 represent two straight lines

Show that the equation 9x² – 24xy + 16y² – 12x + 16y – 12 = 0 represents a pair of parallel lines. Find the distance between them

Show that the equation 4x² + 4xy + y² – 6x – 3y – 4 = 0 represents a pair of parallel lines. Find the distance between them

Prove that one of the straight lines given by ax² + 2hxy + by² = 0 will bisect the angle between the coordinate axes if (a + b)² = 4h²

If the pair of straight lines x² – 2kxy – y² = 0 bisect the angle between the pair of straight lines x² – 2lxy – y² = 0, Show that the later pair also bisects the angle between the former

Prove that the straight lines joining the origin to the points of intersection of 3x² + 5xy – 3y² + 2x + 3y = 0 and 3x – 2y – 1 = 0 are at right angles.