Find the equations of the straight lines each of which passes through the point (3, 2) and cuts off intercepts a and b respectively on x and y-axes such that a – b = 2.

Question

Philoid · Accepted Answer

Concept Used:

The equation of the line with intercepts a and b is

Given:

Here, a – b = 2

⇒ a = b + 2 ……(i)

Explanation:

The line is passing through (3,2).

……(ii)

From equation (i) and (ii)

⇒3b + 2b +4 = b² + 2b

⇒b² – 3b – 4 = 0

⇒ (b – 4)(b + 1) = 0⇒b = 4, -1

Now, from equation (i)

For b = 4, a = 4 + 2 = 6

For b = -1, b = -1 + 2 = 1

Thus the equation of line is

or

⇒x – y = 1 or 2x + 3y = 12