Identify the conic section
Write its equation in standard form
Determine whether it is an ellipse, hyperbola, or parabola
For an ellipse, find the center and the values of (a) and (b)
Compute (c) using (c^2 = a^2 – b^2)
Locate the foci at ((h pm c, k)) or ((h, k pm c)), depending on the major axis
For a hyperbola, find the center and the values of (a) and (b)
Compute (c) using (c^2 = a^2 + b^2)
Locate the foci at ((h pm c, k)) or ((h, k pm c)), depending on the transverse axis
For a parabola, identify the vertex and focus form
Use the standard form to find the focus from the vertex and parameter (p)
For (y^2 = 4px), the focus is ((p, 0))
For (x^2 = 4py), the focus is ((0, p))
Shift the focus coordinates by the center or vertex if the conic is translated
Verify the axis orientation before finalizing the foci