Orthogonal Differentiation?

Question

XY=6 and X^2 - Y^2 =5

how do i prove they're orthogonal in the first quadrant ginen in P(3,2)

Answer 1

In the first quadrant, where x and y are both positive, you can rewrite these as y = 6/x and y = sqrt(x^2 - 5) if x > sqrt(5). In order for two curves to be orthogonal at a point, they need to have opposite reciprocal slope at that point. So use differentiation to find the instantaneous slope of the two curves as (3,2), which should only require use of the x-coordinate 3 (but do verify that both curves pass through the point with that y-coordinate). If the derivatives are opposite reciprocal, the curves are orthogonal.

Answer 2

locate slopes of the two applications on the factor of intersection{via taking the 1st spinoff and locate the fee at factor of inter section} locate the fabricated from slopes. If the product is -a million then they're orthogonal.

Answer 3

xy=6
y=6/x
y'=-6/x^2
y'[3,2]=-6/9
=-2/3...........1
x^2-y^2=5
y^2=x^2-5
2yy'=2x
y'=x/y
y'[3,2]=3/2.....2
from 1&2 we observe
[-2/3]*[3/2]=-1
Product of Slopes at(3,2) for these
curves=-1
Hence ORTHOGONAL