Hello everyone, we are going to talk about.
Case number # 3 .
Case number #3 the Ix is
and Ixy is positive.
So back to our expression tan (2θ)=((-Ixy/(Ix-Iy)/2))
Ixy is positive.
So(-) multiplied by (+) it is (-) divided by (Ix-Iy) which will be negative.
So in the end, we have tan(2θ) is positive but we have to be careful in this case, because our angle
will be negative.
How is that?
That's what we are going to see together again drawing the horizontal X maximum and minimum.
And the Ixy positive pointing downwards.
for our first point starting from the  less value, in this case, will be Ix but always the
sign of Ix and Iy  they are matching we have Ixy positive which means that we are going to draw downward
and Ix of course positive.
So we'll go horizontally Ix and go down for Ixy, we get that point and all was for the Iy we have to
reverse the sign of Ixy.
In that case Iy >Ix.
So we take the value of Iy and coming up because we have negative  that Ixy and we were
locate  point B having coordinate (Iy, -Ixy), always  we are writing reverse
sign of Ixy.
Joining these two lines together A B will intersect with central point O,  and the radius equal SQRt
difference^2, but this time will be.
(((Iy-Ix )/2)^2+Ixy^2)
That will become positive in the end all will have the SQRT of both additions.
This will get R and this is center we draw the circle using at the R-value we will intersect by having
A' and b'  always remember that the direction of X' is the line that is joining the minimum
value with the point or the coordinate that is represented by Ix this will give us this 
X ' is negative sign , What about the 2θ?
the (2θ) is positive Iy z because it is in the in the third to coordinate this is negative
and this is negative that's why tan (2θ) will be positive .
but be careful that the θp, because this angle is twice the angle of this line extension.
That's why this one is negative but not positive, at the end (θp) value will be negative.
or below the x-axis and then the y' This will be enclosed between the positive x and y coordinates
we will proceed to the last case next time thanks and goodbye.
