Pair of Straigh...

Slope of a line is not defined if the line is

The image of the point (α,β) with respect to the line x = y is

Directions: The following question has four choices out of which ONLY ONE is correct.

Consider a line pair ax² + 3xy - 2y² - 5x + 5y + c = 0 representing perpendicular lines intersecting each other at C and forming a triangle ABC with the x-axis.

If the circle x² + y² - 4y + k = 0 is orthogonal with the circumcircle of the triangle ABC, find the value of k.

The point which divides the joint of ( 1, 2 ) and ( 3,4 ) externally in the ratio 1 : 1 .

Above x-axis, the equation of the common tangent to the circle (x - 3)² + y² = 9 and parabola y² = 4x is

The distance of the point ( x , y ) from Y axis is

Directions: The following question has four choices out of which ONLY ONE is correct.

A line passing through P (4, 2) meets the x and the y-axis at A and B respectively. If O is the origin, the locus of the centre of the circumcircle of OAB is

Consider a line pair ax² + 3xy – 2y² – 5x + 5y + c = 0 representing perpendicular lines intersecting each other at C and forming a triangle ABC with the x-axis.

If x₁ and x₂ are intercepts on the x-axis and y₁ and y₂ are the intercepts on the y-axis, the sum (x₁ + x₂ + y₁ + y₂) is equal to

Consider a line pair ax² + 3xy – 2y² – 5x + 5y + c = 0 representing perpendicular lines intersecting each other at C and forming a triangle ABC with the x-axis.

The distance between the orthocentre and circumcentre of the triangle ABC is

The distance between the lines 5x – 12y + 65 = 0 and 5x – 12y – 39 = 0

1. 2

2. none of these

3. - 2

4. 8

The area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 is

The image of the point (α,β) with respect to the line x = y is

If the sum of the slopes of the lines given by x² − 2cxy −7y² = 0 is four times their product then c has the value

Directions: The following question has four choices, out of which ONE or MORE is/are correct.

Lines L₁ : y – x = 0 and L₂ : 2x + y = 0 intersect the line L₃ : y + 2 = 0 at P and Q, respectively. The bisector of the acute angle between L₁ and L₂ intersects L₃ at R and S, respectively. Then,

Let PQR be a right angled isosceles triangle, right angled at P(2, 1). If the equation of the line QR is 2x + y = 3, then the equation representing the pair of lines PQ and PR is

Let P (− 1, 0), Q (0, 0) and R (3, 3) be three points. Then, the equation of the bisector of angle PQR is

A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at the points P and Q respectively. Then the point O divides the segment PQ in the ratio

The lines 2x – 3y = 5 and 6x – 9y – 7 = 0 are

The distance of the point (α,β) from X axis is

1. none of these.

2. α

3. |β|

4. |α|

The line through the points (a , b) and (- a , - b) passes through the point

Directions: The following question has four choices out of which ONE or MORE is/are correct.


It is desired to construct a right angled triangle ABC (C = /2) in xy plane so that it`s sides are parallel to coordinates axis and the medians through A and B lie on the lines y = 3x + 1 and y = mx + 2 respectively. The values of `m`, for which such a triangle is possible, is /are 

The equation of base of an equilateral triangle is x + y = 2 and the vertex opposite to this base is (2, − 1). Then the length of the side of triangle equals

If one of the diagonals of a square is along the line x = 2y and one of its vertices is (3, 0), then its sides through this vertex are given by the equations

A straight line through the point (2, 2) intersects the lines + y = 0 and x − y = 0 at points A and B. The equation of the line AB, so that triangle OAB is equilateral, is

Projection (the foot of perpendicular) from ( x , y ) on the x – axis is