take the derivative of the ellipse equation using implicit differentiation.
The slope of 3x+2y - 5 = 0 is -3/2
so the slope of the perpendicular will be +2/3
set your derivative of the ellipse equal to 2/3 .
You will get a linear equation in x and y
Solve that with the original ellipse equation.
(I would use substituion)
Find the equation of tangent to the ellipse 4x^2+5y^2=20 which are perpendicular to the line 3x+2y-5=0
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