ADVANCED MATHEMATICS FORM 5 – COORDINATE GEOMETRY – part 2

EQUATION OF THE LINE

– Mostly depends on different format those under one of the following

    1.     EQUATION OF A POINT AND SLOPE.

    Let point be and slope be M.

-Let the two points being denoted as A and B

-Consider the figure below

For the line only if

       = 

Multiply by both side

      =

3. EQUATION OF  A SLOPE AND Y – INTERCEPT FORM

–        -Consider the slope and – intercept,

4. EQUATION OF 2 INTERCEPTS FORM

-Let consider X – intercept C, and Y intercept B

5. FAMILY EQUATION

– Is the equation formed from intersection of two lines passing through a certain points.

E.g. equation for intersection of L₁ and L₂ passing through points (a,b) can be obtained by using the formula.

Where K is constant

*
Important steps of determining family equation.

    1.   Solve for K by regarding equations of two lines and the point passing through.

    2.   Form family equation by using the value of K without regarding the point passing through.

Example.

     1.   Find the equation passing through the point (2,3) from the intersection to provided

Solution.

Point

But,

(

From

The equation is