The slope of the line which makes an angle 45^o with the line 3x- y = -5 are:

A line perpendicular to the line 5x - y = 0 forms a triangle with the coordinate axes. If the area of the triangle is 5 sq. units, then its equation is

If a vertex of a square is at the origin and its one side lies along the line 4x + 3y - 20 = 0, then the area of the square is

The equation of the bisectors of the angle between the co-ordinate axes are ______________

The equation of the straight line bisecting the line segment joining the points (2, 4) and (4, 2) and making an angle of 45^o with positive direction of x-axis is ______________

The sum of the squares of the distances of a moving point from two fixed points (a, 0) and (-0, 0) is equal to 2c². Find the equation to its locus.

Find the value of a and p if the equation x-cos a + y sin a = p is the normal form of the line \(\sqrt{3x}+y+2=0\)

A straight line is drawn through the point p(2, 3) and is inclined at an angle of 30° with x-axis. Find the co-ordinates of two points on it at a distance of 4 from P on either side of P.

Find the combined equation of the straight lines through the origin one of which is parallel to and the other is perpendicular to the straight line 3x + y + 5 = 0.

Find the angle between the lines 3x² + 10xy + 8y² + 14x + 22y + 15 = 0.

Show that the lines are 3x + 2y + 9 = 0 and 12x + 8y - 15 = 0 are paralle llines.

Find the equation of the straight line parallel to 5x - 4y + 3 = 0 and having x-intercept 3.

Find the distance between the line 4x + 3y + 4 = 0 and a point  (-2, 4) 

The line 2x - y = 5 turns about the point on it, whose ordinate and abscissae are equal, through an angle of 45° in the anti-clockwise direction. find the equation of the line in the new position.

Show that 3x²+10xy+8y²+14x+22y+15=0 represents a pair of straight lines and the angle between them is tan^-1\(\left( \frac { 2 }{ 11 } \right) \).

If p (r, c) is mid - point of a line segment between the axes, then show that \(\frac{x}{r}+\frac{y}{c}=2\)

Reduce the lines 3x - 4y + 4 = 0 and 4x - 3y + 12 = 0 to the normal form and hence determine which line is nearer to the origin

Find the equation of the line passing through the point of intersection 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x +4y = 7.

For what value of k does 12x²+7xy+ky²+13x-y+3=0 represents a pair of straight lines? Also write the separate equations