Question

A(5,3) and B(3,-2) are two fixed points. find the equation of the locus of P , so that the area of the triangle PAB is 9​

Answer 1

Answer:

5x - 2y = 1  

or  

5x - 2y = 37

Step-by-step explanation:

WE are given that

Area of triangle = 9 unit square

Let us suppose the locus of Point P is ( x , y)

Then

All three vertices's of triangle are following

P (x , y)  , A( 5 , 3)  & B (3 , -2)

And we know that area of triangle can be given as

Area of Δ PAB = (1/2)(| Px(Ay - By)  + Ax(By - Py)  + Bx(Py - Ay) |)

Putting the values we get

      9 = (1/2) | (x(3 -(-2)) + 5(-2 - y) + 3(y - 3)|

⇒  18 = | 5x -10 -5y + 3y - 9|

⇒  18 = | 5x - 2y -19 |

Now we know that according to property of mode their are two possibilities

 5x - 2y -19  = 18

Or

5x - 2y -19  = -18

In the first case

     5x - 2y -19  = 18

⇒        5x - 2y = 37

In the second case

    5x - 2y -19  = -18

⇒        5x - 2y = 1

So

The equation of locus of point P is

5x - 2y = 1  

or  

5x - 2y = 37