Test 4 Memorization Flashcards
What is the standard form of a parabola?
(x-h)^2 = 4p (y-k) (vertical axis) and (y-k)^2 = 4p (x-h) (horizontal axis)
What is the standard equation of a circle?
(x-h)^2 + (y-k)^2 = r^2
What is the general second degree equation?
Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0
What is the standard equation of an ellipse?
(x-h)^2/a^2 + (y-k)^2/b^2 = 1 (Major axis horizontal) or (x-h)^2/b^2 + (y-k)^2/a^2 = 1 (Major axis vertical)
What is the equation to determine foci of an ellipse?
c^2 = a^2 - b^2
How do you find the vertices of an ellipse?
Add/subtract a from the center
How do you find the foci of an ellipse?
Add/subtract c from the center
What is the eccentricity (e) of an ellipse?
c/a
What is the standard equation of a hyperbola?
(x-h)^2/a^2 - (y-k)^2/b^2 = 1 (Transverse axis horizontal) (x-h)^2/b^2 - (y-k)^2/a^2 = 1 (Transverse axis vertical)
How do you find the vertices of a hyperbola?
Add/subtract a from the center
What is the equation to determine foci of a hyperbola?
c^2 = a^2 + b^2
How do you find the foci of a hyperbola?
Add/subtract c from the center
What are the asymptotes for a horizontal transverse axis?
y = k + b/a(x-h) and y = k - b/a(x-h)
What are the asymptotes for a vertical transverse axis?
y = k + a/b(x-h) and y = k - a/b(x-h)
What is the eccentricity (e) of a hyperbola?
c/a
How do you eliminate the parameter?
Solve for t in one equation, substitute into the other equation.
What is the parametric form of the derivative?
dy/dx = dy/dt / dx/dt, where dx/dt != 0
How do you find the second derivative of a parametric?
d/dt[dy/dx] / dx/dt
How do you find the third derivative of a parametric?
d/dt[d^2y/dx^2] / dx/dt
What is the formula for arc length in parametric form?
s = integral a to b of: sqrt((dx/dt)^2 + (dy/dt)^2)
What do the coordinates in a polar coordinate set denote?
r = radius, theta = angle on unit circle
What are the four equations for coordinate conversion of polar coordinates?
x = r cos theta, y = r sin theta, tan theta = y/x, x^2 + y^2 = r^2
What is the equation for the slope of the tangent line to the graph of r = f(theta)?
r cos theta + r’ sin theta / r’ cos theta - r sin theta
How do you find tangent lines of a polar function at the pole?
If r(alpha) = 0 and r’(alpha) = 0 then the line theta = alpha is tangent at the pole to the graph of r = f(theta).
What is the formula for area of a region in polar coordinates (radial lines)?
A = 1/2 integral a to b of: r^2 d(theta)
What is the formula for arc length of a polar curve?
s = integral a to b of: sqrt(r^2 + (dr/dtheta)^2) dtheta
What is L’Hopital’s rule?
If direct substitution produces an indeterminate form, then Lim x->c f(x)/g(x) = Lim x->c f’(x)/g’(x)
What are the indeterminate forms?
0/0, infinity / infinity, 0 * infinity, 1 ^ infinity, 0 ^ 0, infinity - infinity
