Posted by Lance on Monday, January 7, 2013 at 5:05pm.
What is the equation of a line through (2,5) and whose segment intercepted between the axes in the 2nd quadrant is 7sqrt2?
Please help me solve this

Geometry  Reiny, Monday, January 7, 2013 at 7:02pm
Where are you getting these ?
let P be (2,5)
let the xintercept be A(x,0) and the yintercept be B(0,y)
so first of all:
x^2 + y^2 = (7√2)^2 = 98
now the slope of AP = slop BP
(y5)/(2 = 5/(x+2)
crossmultiplying and rearranging I got
xy + 2y = 5x
y(x+2) = 5x
y = 5x/(x+2)
sub that into above:
x^2 + y^2 = 98
x^2 + 25x^2/(x+2)^2 = 98
x^2(x+2)^2 + 25x^2 = 98(x+2)^2
expanding all this and simplifying I got the horrible equation
x^4 + 4x^3  69x^2  392x  392 = 0
at this point I "cheated" and ran it through Wolfgram
http://www.wolframalpha.com/input/?i=x%5E4+%2B+4x%5E3++69x%5E2++392x++392+%3D+0
to get an exact value of x = 7
so y = 35/(5) = 7
we can now find the slope of our line which is
(50)/(2+7) = 1, wow!
equation is
y = x + 7
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