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 triangle pab is 9
​

Answer 1

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

Let say Point P ( x , y)

P (x , y)  , A( 5 , 3)  & B (3 , -2)

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

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

=> 18 = | 5x -10 -5y + 3y - 9|

=> 18 = | 5x - 2y -19 |

Case 1 :  5x - 2y -19  = 18

=> 5x - 2y = 37

Case 2 5x - 2y -19  = -18

=> 5x - 2y = 1