geometry
posted by karan on .
find k if one of the lines given by kx^2+10xy+8y^2=0 is perpendicular to 2xy=5

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.