*Circle The locus of a point P (x, y) which moves in a plane so that its distance from a fixed point is always a constant.  The fixed point is called the centre C (u, v) of the circle and the constant  distance is called its radius (R).

Also a radius of a circle is a straight line joining the centre any point on the circumference. As CP = R, thus using displacement formula we can write

The above expression is called Central form of a circle.

A circle can also be expressed as

ax² + by² + 2 gx + 2 fy + c = 0

This expression is called general form of a circle.

Here (-g, -f) is the center of the circle

is radius

If centre of a circle coincides with origin O (0, 0) then the above expression can be written as,

x² + y² = R².              

This expression is called Standard form of a circle.

*Harmonic progression

If a, a + d, a + 2d, _ _ _ _ _ _ _ are in AP, then their reciprocals are in harmonic progression (HP).

*Slope of a straight line

• Slope (symbol, m) of a straight line is defined as the tan of the anticlock wise angle made by that line with the positive horizontal axis.
• i.e. m = tan θ             
• As tan θ can have any real value, so we can say
• 
• Slope of a straight line passing through points A (x₁, y₁) & B (x₂, y₂) is given by
• 
• Here Δx, Δy represents change in x & y coordinates respectively.
• If two lines are ||, then their slopes are equal.
• If two lines are perpendicular then the product of their slope is – 1.

*Expansion formulae

sin (A ± B) = sin A cos B ± cos A sin B

cos (A ± B) = cos A cos B ± sin A sin B