Question

2
If
(2,-6) and (-3,-5) lie on the locus ax +by= 1. Then a and b
are​

Answer 1

We have to find the value of a and b if (2, -6) and (-3, -5) lie on the locus of ax + by = 1.

solution : case 1 : (2, -6) lies on the locus of ax + by = 1

then, a(2) + b(-6) = 1

⇒2a - 6b = 1 ...(1)

case 2 : (-3, -5) lies on the locus of ax + by = 1

then, a(-3) + b(-5) = 1

⇒3a + 5b = -1 ...(2)

doing 3 × eq (1) - 2 × eq (2) we get,

3(2a - 6b) - 2(3a + 5b) = 3 - 2(-1) = 5

⇒6a - 18b - 6a - 10b = 5

⇒-28b = 5

⇒b = -5/28

and a = (1 + 6b)/2 = (1 - 30/28)/2

= -1/28

therefore the value of a and b are -1/28 and -5/28 respectively.