General second-degree equation and conic classification
Two-dimensional geometry · Mathematics
Study notes
Q: Classify: (a) x²−4y²=0 (b) x²+y²−4=0 (c) x²+2xy+y²−1=0. (a) a=1,b=−4,h=0: h²−ab = 4 > 0, Δ=0: pair of lines (x=±2y) - degenerate hyperbola. (b) a=b=1,h=0: circle. (c) h²−ab = 1−1 = 0, Δ=0: pair of parallel lines (x+y=±1) - degenerate parabola.