Question

The line x/a - y/b = 1, where a and b are positive constants, meets the x-axis at P and the y-axis at Q. The gradient of the line PQ is 2/5 and the length of the line PQ is 2√29. Find the value of a and the value of b.

Answer 1

Step-by-step explanation:

OQ= b units.

In right angled triangle POQ , OP^2+OQ^2= PQ^2. or, a^2+b^2 = 45. ………………..(1)

Slope of the line PQ (x/a+y/b=1) = -b/a. , thus -b/a = -1/2. Or, a = 2b……………..(2)

Putting a=2b in eqn. (1).

4b^2+b^2= 45.

or, 5b^2=45

or, b^2 = 45/5=9.

or, b= +3 , - 3(not valid as -ve).

And a= 2b = 2×3=6.

Thus, a= 6 units , b= 3 units. Answer