Calculus or advanced algebra circle problem?
A triangle is being enscribed inside a circle x^2+y^2=25 so the the vertices are at points (0,-5), (x,y), (-x,y). Calculate the maximum possible area of the triangle.
We're suppose to solve this by finding the derivative of the area equation I suppose. I'f its quadratic this could be solved by finding he vertices of the the quadratic. I don't know how to find such equation.
Can x be isolated by taking the square root of 25-y^2 ? Is x=5-y ?
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Pretty sure it's 75*root(3) / 4
Area = (1/2)*b*h
A = (1/2)*(2x)*(y + 5)
A = x*[root(25 - x^2) + 5]
A' = root(25 - x^2) - x^2/root(25 - x^2) + 5
Set equal to zero:
x = 5root(3) / 2
Area = 75root(3) / 4
Base is the horizontal length at the top, 5root(3)
Height is from the midpoint of that segment to the vertex at the bottom (at (0, -5)), 15/2
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