Prove that the curves x = y2 and xy = k cut at right angles if 8k2 = 1. [Hint: Two curves intersect
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from x = y^2,find slope = m1 = dy/dx = 1/2y
from xy = k, find slope = m2 = dy/dx = - y/x
tan theta = |(m1-m2) /(1+m1m2)|
theta = 90
so m1m2 = - 1
put values of m1 and m2
find point of intersection by using givn eqs. and proceed.
from xy = k, find slope = m2 = dy/dx = - y/x
tan theta = |(m1-m2) /(1+m1m2)|
theta = 90
so m1m2 = - 1
put values of m1 and m2
find point of intersection by using givn eqs. and proceed.
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