# Geometry

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What is the equation of a line through (-2,5) and whose segment intercepted between the axes in the 2nd quadrant is 7sqrt2?

• Geometry -

Where are you getting these ?

let P be (-2,5)
let the x-intercept be A(x,0) and the y-intercept be B(0,y)

so first of all:
x^2 + y^2 = (7√2)^2 = 98

now the slope of AP = slop BP
(y-5)/(2 = -5/(x+2)
cross-multiplying and re-arranging 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
(5-0)/(-2+7) = 1, wow!

equation is

y = x + 7

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