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.

Question

The gradient of PQ is 2/5, and it's length is 2√29.

Can you help me find the value of a and the value of b?

Answer 1

HInt:

So, the intercepts are $(a,0);(0,-b)$

$\implies(a-0)^2+(0+b)^2=(2\sqrt{29})^2$

and $y=\dfrac abx-b\implies$ gradient is $\dfrac ab$