A line passes through the point (2, 2) and is perpendicular to the line 3x + y = 3. Its y intercept is ______.

The area of a triangle whose vertices are (3, -2), (5, 6) and (-2, -5) is ______.

If p be the length of the perpendicular from the origin to the line \({x\over a}+{y\over b}=1\) then ______.

The angle between the lines 3x - 2y + 5 = 0 and 2x + 3y - 7 = 0 is ______.

The vertices of a triangle are (6, 0), (0, 6) and (6, 6). The distance between its circumcentre and centriod is ______.

Using the distance formula show that the points A(3,-2), B(5,2) and C(8,8) are collinear.

Find the area of \(\triangle \)ABC, the mid-points of whose sides AB,BC and CA  are D(3,-1),E(5,3) and F(1,-3), respectively.

Reduce the following equation into slope intercept form and find their slopes and the y-intercepts y=0.

Find the equation of a line, whose inclination with X - axis is 150\(^{o}\)   and which passes through the point (3, - 5).

The equation of two sides of a square are 5x - 12y - 65 = 0 and 5x - 12y + 26 = 0. Find the area of a square.

Find the equations of the medians of a triangle, the coordinates of whose vertices are (-1, 6), (-3, -9) and (5, -8).

Find the transformed equal to x ²+2x - 2y²+2 = 0 when the orgin is shifted to (-3, 2).

Find the point on X-axis which is equidistant from the points(3,2) and(-5,-2).

Two lines passing through the point (2, 3) intersects each other at an angle of 60o . If slope of one line is 2, find equation of the other line.

If p is the length of perpendicular from the origin on the line \(\frac { x }{ a } +\frac { y }{ b } =1\) and a² , p² and b² are in AP, then show that a⁴ + b⁴ = 0. 

Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).

find the transformed equation of the circle x²+y² = 9 when the origin is shifted to (-1, -3).

Find the equation of the line passing through the intersection of the lines 2x - y + 3 = 0 and x + 2y + 1 = 0 and parallel to y-axis.

Find the equations of two straight lines which are at a distance 1/2 from the origin and passes through the point (0,1)

Find the equation of the ellipse \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1\) when the origin is shifted to (-3, 2).

Find the equations of the medians of a triangle formed by the lines x + y - 6 = 0, x - 3y - 2 = 0 and 5x - 3y + 2 = 0.

Find the equation of line passing through the point of intersection of lines x-7y+5 = 0 and 3x+y-7=0 and perpendicular to the line 2x-5y+1 = 0.