Solve 3-(x-5)=y^2

Identify the conic

Find the standard equation of the parabola

Find the vertex of the parabola

Find the focus of the parabola

y^{2} = - (x - 8)

Show Solution

Solve for x

Solve for y

x = - y^{2} + 8

Show Solution

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Not symmetry with respect to the origin

Show Solution

Find the derivative with respect to x

Find the derivative with respect to y

\frac{d y}{d x} = - \frac{1}{2 y}

Show Solution

Find the second derivative with respect to x

Find the second derivative with respect to y

\frac{d ^{2} y}{d x ^{2}} = - \frac{1}{4 y ^{3}}

Show Solution

r = - \frac{cos ( θ ) + 31 sin ^{2} ( θ ) + 33}{2 sin ^{2} ( θ )} r = \frac{- cos ( θ ) + 31 sin ^{2} ( θ ) + 33}{2 sin ^{2} ( θ )}

Show Solution