Analytic Geometry

analytic geometry asymptotes Ax² axis parallel Bisecting chords central conic chord of contact circle x² conic section conic x² constant contact corresponding coördinate planes cylinder determine diameter directing curve direction cosines directrix Draw the figure ellipse Example Find the equation Find the locus find the points Find the tangents fixed point foci formula geometrically given line given point Hence hyperbola imaginary latus rectum line 3x line joining line x method moving point ordinates origin P₁ parabola y² parallel to Ox passing perpendicular point moves points at infinity points of intersection points P1 positive quadratic quadric radical axis radius vector represents rotation of axes second degree segment slope Solve Ex straight line Substituting surface symmetric with respect term theorem of Ex touches the line trace the curve transverse axis values vertex vertices Write the equation x-axis y-axis y-intercept y₁