#How to solve this problem using calculus?

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rustic mountain
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I know the derivative is equal to -x/4y
which is the slope of the tangent line
That is passing
-5,0

image.png
rustic mountain
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solved it
substituting that at point x1,y1
the tangent line has a slope of
dy/dx = -x1/4y1

at the point (-5,0)
the slop can also be equal to
y1 / (x1 + 5)

this give us the relationship
4y1^2 = -x1^2 -5x1

we can now solve the original ellipse equation at point x1,y1
4y1^2 +x1^2 = 5 , => 4y1^2 = 5-x1^2

then we have equality on both sides
-x1^2 - 5x1 = 5 -x1^2 , => -5x1 = 5
x1 = -1
y1 = 1
slope = 1/4
the line equation is
y = mx + b
at -5,0
0 = 1/4 *-5 + b
b = 5/4
y = x/4 + 5/4
at x = 3
y = 2