25x2 + 4y2 100x + 8y 96 = – – 0 Ax2 - By2 + Cx + Dy + E = 0 (coefficients of x2 & y2 opposite signs) Ex: 4x2 9y2 18y 45 = 0 – – – By2 Ax2 + Cx + Dy + E = 0 – (coefficients of x2 & y2 Ex: opposite signs) x2 y2 2x 8y 11 = 0 – – – – Identifying Quadratic (and Linear) Equations For each equation, tell what shape it is (line, circle, parabola, ellipse, hyperbola). x2 6x + 4y2 + 8y 4 = 0 – – x2 6x 4y2 + 8y 4 = 0 – – – x2 8x + y2 + 2y + 5 = 0 – x y = 9 – x2 y = 9 – x2 y2 = 9 – x2 + y2 = 9 x2 + 9y2 = 9 4x2 + 8y2 = 32 x = 16y2 32 –
25x2 + 4y2 – 100x + 8y – 96 = 0 Ex: Ax2 - By2 + Cx + Dy + E = 0 (coefficients of x2 & y2 opposite signs) 4x2 – 9y2 – 18y – 45 = 0 Ex: By2 – Ax2 + Cx + Dy + E = 0 (coefficients of x2 & y2 opposite signs) x2 – y2 – 2x – 8y – 11 = 0 Identifying Quadratic (and Linear) Equations For each equation, tell what shape it is (line, circle, parabola, ellipse, hyperbola). x2 – 6x + 4y2 + 8y – 4 = 0 x2 – 6x – 4y2 + 8y – 4 = 0 x2 – 8x + y2 + 2y + 5 = 0 x – y = 9 x2 – y = 9 x2 – y2 = 9 x2 + y2 = 9 x2 + 9y2 = 9 4x2 + 8y2 = 32 x = 16y2 – 32