The point of intersection of diagonals of a square ABCD is at the origin and one of its vertices is at A(4, 2). What is the equation of the diagonal BD?

What is the other end of the diameter of the circle x² + y² = 9 whose one end is (2, √5)?

If A, B and C are in AP, then the straight line Ax + 2By + C = 0 will always pass through a fixed point. The fixed point is

The graph of the equation x - 7y = -42, intersects the y-axis at P (α, β) and the graph of 6x + y - 15 = 0, intersects the x-axis at Q (γ, δ). What is the value of α + β + γ + δ ?

The equation of the circle whose diameter lies on 2x + 3y = 3 and 16x – y = 4 which passes through (4, 6) is

What is the equation of the line passing through origin and perpendicular to the plane 3x + 2y + 5z = 0?

The graphs of the equations 

4x+\(\frac{1}{3}\)y=\(\frac{8}{3}\)and \(\frac{1}{2}\)x+\(\frac{3}{4}\)y +\(\frac{5}{2}\)=0 intersect at a point P. The point P also lies on the graph of the equations:-

What is the radius of the circle given by the equation x² + 14x + y² – 2x + 25 = 0?

The straight lines x + y – 4 = 0, 3x + y – 4 = 0 and x + 3y – 4 = 0 form a triangle, which is

Find the coordinates of point that divides the line joining the points A (2, 5) and B (-1, 8) in ratio 3 : 2 externally.

A circle is drawn to cut a chord of length 2a units along X-axis and to touch the Y-axis. The locus of the centre of the circle is

Find the coordinates of the point which divides the line segment joining the point (-1, 2) and (2, 3) in the ratio of 2 : 1.

The equation of the line passing through the point (2, 3) and the point of intersection of lines 2x – 3y + 7 = 0 and 7x + 4y + 2 = 0 is

Let α be the distance between the lines -x + y = 2 and x – y = 2, and β be the distance between the lines 4x – 3y = 5 and 6y – 8x = 1, then

The graph of the equations 2x + 3y = 11 and x - 2y + 12 = 0 intersects at P(x₁, y₁) and the graph of the equation x - 2y + 12 = 0 intersects the x-axis at Q(x₂, y₂). What is the value of (x₁ - x₂ + y₁ + y₂) ?

The points (1, 3) and (5, 1) are two opposite vertices of a rectangle. The other two vertices lie on the line y = 2x + c. What is the value of c?

In what ratio does the line 2x - y = 3 divide the line segment joining the points (2, 3) and (3, -2)?

If the lines y + px = 1 and y – qx = 2 are perpendicular, then which one of the following is correct?

If the coordinates A (2, 3), B (0, 5) and C (6, 1) are that of three vertices of a rectangle, then what is the coordinate of the fourth vertex?

The point of intersection of the graphs of the equations 3x - 5y = 19 and 3y - 7x + 1 = 0 is P(α, β). What is the value of (3α - β)? 

In the circle x² + y² = 4, a diameter was drawn from (√2, √2) on the circle. What are the equations of the tangent parallel to this diameter?

At what points of the curve \(y = \frac{2}{3}{x^3} + \frac{1}{2}{x^2},\) tangent makes the equal angle with axis

In which quadrants do abcissa and ordinate have different signs?

Find the coordinate of the foot of perpendicular from the point (1, 0) to the line -x + y = 0.

For what value of C₂, the system of equation 6x + 2y = 2 & 3x + y = C₂ will be coincident?

Circles are drawn through the point (2, 0) to cut intercept of length 5 units on the x-axis. If their centres lie in the first quadrant, then their equation is

The point (1, -1) is one of the vertices of a square. If 3x + 2y = 5 is the equation of one diagonal of the square, then what is the equation of the other diagonal?

The angle between the straight lines \(\frac{x-2}{2}=\frac{y-1}{5}=\frac{z+3}{-3}\) and \(\frac{{x + 1}}{{ - 1}} = \frac{{y - 4}}{8} = \frac{{z - 5}}{4}\)

A circle is drawn on the chord of a circle x² + y² = a² as diameter. The chord lies on the line x + y = a. What is the equation of the circle?

If the point of intersection of lines x + y = 2 and 2x - y = 1 lies on y = kx + 5. What is the value of k?

The graphs of the equations 7x + 11y = 3 and 8x + y = 15 intersect at the point P, which also lies on the graph of the equation:

In which quadrant does the point (4, -16) lies?

If a line 2x - y - 6 = 0 intersects the other line joining the points (3, 2) and (1, 2) in the ratio k : 1, then find the value of k.

If P(3, 2) and Q(5, 8) are the two coordinates of any two points on a line. Find the slope of the line. 

Find the coordinates of the points where the graph 57x-19y=399 cuts the coordinate axes.

At which point does two lines 5x + 7y = 14 and 3x – 2y = 27 meets?

At which point does two lines 5x + 7y = 14 and 3x – 2y = 27 meets?

Find the distance between the two points X(4, -3) and Y(6, 2).

The graphs of the linear equations 4x - 2y = 10 and 4x + ky = 2 intersect at a point (a, 4). The value of k is equal to:

If a line 2x - y - 6 = 0 intersects the other line joining the points (3, 2) and (1, 2) in the ratio k : 1, then find the value of k.

Find the slope of the line passing through the points (−3, 5) and (5, −1).
 

In what ratio does the line 2x - y = 3 divide the line segment joining the points (2, 3) and (3, -2)?

The graphs of the linear equations 3x - 2y = 8 and 4x + 3y = 5 intersect at the point P(α,β). What is the value of (2α - β)

What is the reflection of the point (5, -3) in the line y = 3?

Find the coordinate of the point which will divide the line joining the point (2, 4) and (7, 9) internally in the ratio 1 : 2.

Find the distance of the point P(20, 21) from the origin.

For what value of k will the lines 2x + 7ky – 8 = 0 and x + y – 9 = 0 have no solution?

For what value of k, do the equations 3x - y + 8 = 0 and 6x - ky = - 16 represent coincident lines?

Which of the following is the sum of the values of a and b if the equations 2x + y = a, 8x + by = 12 have infinite solutions?

If the equations 14x + 8y + 5 = 0 and 21x - ky - 7 = 0 have no solution, then the value of k will be _____.