**– Equation of the straight line**

The equation of a straight line is

y=mx+b where m is the gradient and b is the y-intercept.

The equation of a tangent to a curve is

y – f(x_{0}) = f'(x_{0})(x – x_{0})

f'(x_{0}) is the slope of the line at the point x_{0 }and passes through the point (x_{0 , }f'(x0))

If the slope of 2 lines are m=m’, the lines are parallel

If the slope of 2 lines are m= – \(\frac{1}{m'}\) , the lines are perpendicular

** – The circle**

The equation of the circle with center (h,k) and radius r is

(x – h)^{2} + (y – k) ^{2}= r^{2}

The general equation of the circle is

x^{2} + y^{2} + 2gx + 2fy + c = 0

The center of the circle and the radius can be obtained by completing the square.

The angle in a semicircle is a right angle.

The perpendicular from the center of a circle to a chord bisects the chord.

The radius of a circle is perpendicular to the tangent at its point of intersection.

**– Parametric Equations**

The parametric equations describes a circle center O and radius =2

The equations describes a circle center (3,-2) and radius 4

The equations describes the rectangular hyperbola xy = 9

{ y =\(\frac{3}{t}\)

**– Modelling with parametric equations**

Use of parametric equations in kinematics (Parabolic trajectory)

**-Conversion of cartesian coordinates to polar coordinates**

and \(x^2 + y^2\)