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Magazine Problem 324
For the following exercises, rewrite the given equation of the quadric surface in standard form. Identify the surface. \(8 x^{2}-5 y^{2}-10 z=0\)
Problem 325
For the following exercises, rewrite the given equation of the quadric surface in standard form. Identify the surface. \(x^{2}+5 y^{2}+3 z^{2}-15=0\)
Problem 326
For the following exercises, rewrite the given equation of the quadric surface in standard form. Identify the surface. \(63 x^{2}+7 y^{2}+9 z^{2}-63=0\)
Problem 327
For the following exercises, rewrite the given equation of the quadric surface in standard form. Identify the surface. \(x^{2}+5 y^{2}-8 z^{2}=0\)
Problem 328
For the following exercises, rewrite the given equation of the quadric surface in standard form. Identify the surface. \(5 x^{2}-4 y^{2}+20 z^{2}=0\)
Problem 329
For the following exercises, rewrite the given equation of the quadric surface in standard form. Identify the surface. \(6 x=3 y^{2}+2 z^{2}\)
Problem 330
For the following exercises, rewrite the given equation of the quadric surface in standard form. Identify the surface. \(49 y=x^{2}+7 z^{2}\)
Problem 331
For the following exercises, find the trace of the given quadric surface in the specified plane of coordinates and sketch it. [T] \(x^{2}+z^{2}+4 y=0, z=0\)
Problem 332
For the following exercises, find the trace of the given quadric surface in the specified plane of coordinates and sketch it. [T] \(x^{2}+z^{2}+4 y=0, x=0\)
Problem 333
For the following exercises, find the trace of the given quadric surface in the specified plane of coordinates and sketch it. [T] \(-4 x^{2}+25 y^{2}+z^{2}=100, x=0\)
