Question

Find x in terms of a so that the line joining the points (x, x/a), (a, a/x) shall have a slope of 1

Answer 1

Slope:


m = (y2 - y1)/(x2 - x1)


m = (a/x - x/a)/(a - x)


m = (a^2/ax - x^2/ax)/(a - x)


m = ((a^2 - x^2)/ax)/(a - x)


m = (a^2 - x^2)/(ax(a - x))


m = ((a - x)(a + x))/(ax(a - x))


m = (a + x)/(ax)


1 = (a + x)/(ax)


Now solve for x

Answer 2

@jim_thompson5910 a=(x)/(x-1) ?

Answer 3

you want to solve for x, not 'a'

Answer 4

x=a/(a-1)?

Answer 5

yes

Answer 6

thanks