For what value of m will the system of equations 18x - 72y + 13 = 0 and 7x - my - 17 = 0 have no solution?

For what value of m will the system of equations 17x + my + 102 = 0 and 23x + 299y + 138 = 0 have infinite number of solutions?

What is the distance of origin from the plane  x + y + z = 1?

Two lines A and B pass through the origin. A passes through (2, 1) whereas B passes through (3, 1). What is the measure of the angle between the lines?

If the equation of the directrix of a parabola is 2x + y = 5 and the focus of the parabola is (8, 1), then what is the equation of the axis of the parabola?

For the line 5x + 3y = 30, what is the sum of x and y intercepts?

A and B are two straight lines passing through origin and inclined by 60° with respect to each other. If y = √3x bisects the minor angle formed between the lines, then the equation of the pair of lines is ______________

What is the distance of the point (3, 2) from the directrix of the parabola y² = 12x?

What is the equation of pair of lines passing through origin and inclined to the y axis by 30° (both clockwise and anti-clockwise)?

The equation of line perpendicular to x + 3y = 0 and passing through origin is ___________.

What is the equation of the straight line (in xy plane) which is at a distance of 5 units from the origin and the normal to the line from origin makes an angle of 30° with x axis?

A Cartesian system is changed by shifting the x-axis 3 units upwards and the y-axis 2 unit leftwards. If the new coordinate of a point is (5, 1), then what is the distance of the point from the origin in old coordinate system?

If x + y = 0 and x – y = 0 becomes the coordinates axes instead of x = 0 and y = 0, what will be the new coordinates of the point (0, 1)?

If the coordinates of the focus and the vertex of a parabola are (8, 1) and (3, 0) respectively, then what is the equation of the directrix of the parabola?

√ {(x – x₁)² + (y – y₁)²} - √ {(x – x₂)² + (y – y₂)²} = constant, where (x₁, y₁) and (x₂, y₂) are two fixed points represents the equation of a/an _________________

√ {(x – 8)² + (y – 2)² + (z – 5)^2} = 3 units. What is the locus of all the points which satisfies the above equation?

If the line 

is perpendicular to the plane 3x + by + 5z = 17, then what is the value of a² + b²?

Find the equation of the ellipse, with a major axis along the x-axis and passing through the points (2, 3) and (-3, 4).

If the coordinates of the focus and the vertex of a parabola are (8, 1) and (3, 0) respectively, then what is the equation of the directrix of the parabola? 

What is the general equation of the plane containing z axis?

Where does the line x/3 = y/4 = z/5 meet the plane 3x + 4y + 5z = 50?

What is the equation of the plane which passes through the following points?

A (1, 2, 0), B (2, 3, 0) and C (4, 4, 0)

(3x + 4y + 5) /5 = √ {(x – 3)² + (y – 4)²} is the equation of a parabola. What are the coordinates of focus of the parabola?

The equation of line, which bisect the line joining two points (2, –19) and (6, 1) and perpendicular to the line joining two points (–1, 3) and (5, –1), is

The circle x² + y² + 4x – 7y + 12 = 0, cuts an intercept on y-axis equal to

If a and b are two arbitrary constants, then the straight line  \((a - 2b)x + (a + 3b)y + 3a + 4b = 0\) will pass through 

The intercept on the line y = x by the circle x² + y² - 2x = 0 is AB, equation of the circle on AB as a diameter is

The equation of line passing through point of intersection of lines 3x - 2y - 1 = 0 and x - 4y + 3 = 0 and the point (π, 0), is

The equation of the circle concentric with the circle x² + y² - 4x - 6y - 3 = 0 and touching y-axis, is

The distance of the point (1, 3) from the line 2x + 3y = 6, measured parallel to the line 4x + y = 4, is

The distance of the point (2, 3, 4) from the line \(1 - x = \frac{y}{2} = \frac{1}{3}(1 + z)\) is

The equation of straight line which cuts off an intercept of 5 units on negative direction of y-axis and makes an angle 120^o with positive direction of x-axis is

One diagonal of a square is along the line 8x - 15y = 0 and one of its vertex is (1, 2). Then the equation of the sides of the square passing through this vertex, are

The equations of the lines through the point of intersection of the lines x - y + 1 = 0 and 2x - 3y + 5 = 0 and whose distance from the point (3, 2) is 7/5, is

A straight line \((\sqrt 3 - 1)x = (\sqrt 3 + 1)y\) makes an angle \({75^o}\) with another straight line which passes through origin. Then the equation of the line is

Equation of the line which passes through the point (-4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5 : 3 by this point, is

The length of the perpendicular drawn from the point (5, 4, –1) on the line \(\frac{{x - 1}}{2} = \frac{y}{9} = \frac{z}{5}\) is

The equations of the circles touching both the axes and passing through the point (1, 2) are

The equation of the circle passing through the point (2, 1) and touching y-axis at the origin is

The angle between the lines x + y – 3 = 0 and x – y + 3 = 0 is α and the acute angle between the lines x - √3y -2√3y + 2√3 = 0 and √3x – y + 1 = 0 is β. Which one of the following is correct?

The two circles \({x^2} + {y^2} - 2x + 22y + 5 = 0\) and \({x^2} + {y^2} + 14x + 6y + k = 0\) intersect orthogonally provided k is equal to

The locus of the centre of circle which cuts the circles \({x^2} + {y^2} + 4x - 6y + 9 = 0\) and \({x^2} + {y^2} - 4x + 6y + 4 = 0\) orthogonally is

The position of the points (3, 4) and (2, –6) with respect to the line \(3x - 4y = 8\) are

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:-

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

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