Angle Between Two Lines:

This formula helps to find the angle between two lines when the slopes are known. Here, $m_1$ represents the slope of line 1 and $m_2$ represents the slope of line 2.
1. $tan \theta = \left ( \pm \dfrac{m_1 - m_2}{1 + m_1.m_2} \right )$

When two lines are perpendicular then the slopes of the lines are in the following relation:
1. $m_1 × m_2 = -1$

When two linds are parallel to each other then the slopes of the lines are in the following relation:
1. $m_1 = m_2$




Pair Of Straight Lines:

The equation that represents homogeneous equation of second degree of pair of lines is
1. $ax²+2hxy+by² = 0$

The equation that represents general equation of second degree of pair of lines is
1. $ax² +2hxy+by²+2gx+2fy+c=0$

The angle between two pair of lines in homogeneous equation can be known by:
1. $tan \theta = \left ( \pm \dfrac{2 \sqrt{h²-ab}}{a+b} \right )$




Circle:

The general equation of a circle is
1. $x² +y² +2gx +2fy +c = 0$

The equation of a cirlce having centre at (0,0) is
1.$x² +y²= r²$

The equation of circle having centre at (h,k) is
1. $(x-h)² + (y-k)²= 0$

The equation kf a circle in diameter form is
1. $(x-x_1)(x-x_2) + (y-y_1)(y-y_2) = 0