Question

If points P(x, y) , A(a, 0) and B(0, b) are collinear Divya Kota: (a) x + y = ab (b) ax + by = ab (c) bx + ay – ab = 0 (d) None​

Answer 1

Answer:

Let the points be A(x,y), B(a,0) and C(0,b). As the points are collinear.

Area of triangle ABC is zero .

The condition for collinearity of three given points (x1,y1),(x2,y2) and (x3,y3) is

x1(y2-y3) + x2(y3-y1) + x3(y1-y2) = 0.

Thus, x(0-b) + a(b-y) + 0(y-0) = 0.

⇒ -bx + ab - ay = 0

⇒ bx + ay = ab

⇒ bx/ab + ay/ab = 1.

⇒ x/a + y/b = 1.