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

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.

Choose the correct alternative:
Equation of the straight line that forms an isosceles triangle with coordinate axes in the I-quadrant with perimeter `4 + 2sqrt(2)` is

Choose the correct alternative:
The coordinates of the four vertices of a quadrilateral are (−2, 4), (−1, 2), (1, 2) and (2, 4) taken in order. The equation of the line passing through the vertex (−1, 2) and dividing the quadrilateral in the equal areas is

Choose the correct alternative:
If the equation of the base opposite to the vertex (2, 3) of an equilateral triangle is x + y = 2, then the length of a side is

Choose the correct alternative:
The image of the point (2, 3) in the line y = −x is

Choose the correct alternative:
The length of ⊥ from the origin to the line `x/3 - y/4` = 1 is

Choose the correct alternative:
The area of the triangle formed by the lines x² – 4y² = 0 and x = a is

Choose the correct alternative:
If one of the lines given by 6x² – xy – 4cy² = 0 is 3x + 4y = 0, then c equals to ______.