Posted by karan on Saturday, March 2, 2013 at 5:08am.
find k if one of the lines given by kx^2+10xy+8y^2=0 is perpendicular to 2xy=5

geometry  Reiny, Saturday, March 2, 2013 at 8:09am
The slope of 2xy=5 is 2
So the slope of a perpendicular line is 1/2
kx^2 + 10xy + 8y^2 = 0 is supposed to be the intersection of 2 straight lines, so let's solve it for y
y = (10x ± √(100x^2  32kx^2) )/16
= (10x ± x√10068k)/16
= x(10 ± √(10032k) )/16
So the slope of the two lines is (10 ± √(10032k) )/16
thus:
(10 ± √(10032k) )/16 = 1/2
20 ± 2√10032k = 16
±2√10032k = 4
±√10032k = 2
square both sides
10032k = 4
32k=96
k=3
check my arithmetic.
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