Reduce the equation : x2 – y2 – z2 +2x -2y -4z + 2 = 0 to standard form and then classify the surface?

2 Answers

• (x-1)^2 / 2 - (y-1)^2 /2 + (z+2)^2 / 2 =1

  Hyperbloid

• For a conventional quadratic A*x^2 + B*x*y + C*y^2 + D*x + E*y + F = 0 if B^2 - 4AC < 0 ellipse if B^2 - 4AC = 0 parabola if B^2 - 4AC > 0 hyperbola For our equation A = a million, B = 0, C = 0 So B^2 - 4AC = 0 and we've a parabola. the classic type for a parabola with an x^2 time period is (x - h)^2 = 4*p*(y-ok) for parabola with vertex (h,ok) and directrix y = ok-p So we ought to finish the sq. interior the given equation. (x^2 + 2x + a million) + y - 2 = 0 Isolate the proper sq. (x + a million)^2 = - (y - 2) this ability our center is (-a million,2) and our directrix is y = 2 + a million/4 = 9/4