Suppose a surface in three-dimensional space has the equation ax^2+bx+cy^2+dy=z  and it contains the points (1,1,1), (1,2,2), (2,-1,-2), and (3,-2,3). Set up a system of linear equations and use row reduction to determine the coefficients for this equation.

Q: Find the parabola of the form y=ax^2+b which best fits the points (1,0), (4,4), (6,8) by minimizing…

A:

Q: How far is the center equation 10x^2 -y^2 -5y -11 to its focus?

A: Note: It is assumed that the equation, 10x2-y2-5y-11 is 10x2-y2-5y-11=0.   The conics are generated…

Q: Find the solution of the nonlinear system below f1= x^2-xy+y^2-3, f2=x+y-xy *

A: Consider the projections of f1 and f2 on xy plane...

Q: Given the equation 9x^2 + 199 + 100y = 108x-25y^2, it is verified that its center (h, k) and…

A: Given the equation 9x2+199+100y=108x-25y2

Q: Show that the point (5,4,2), (6,2,-1) and (8,-2,-7) are collinear

A:

Q: write the equation of the quadraticfunction whose graph is a parabola containing the givenpoints

A: Let the equation of the quadratic function be: fx=y=ax2+bx+c This function passes through the points…

Q: the center and foci of the followin 4x^(2)+8y^(2)-16x+32y+32=0

A: Given,              4x2+8y2-16x+32y+32=0. To find the center and foci of the given equation.

Q: Determine if (3, -1, 4) is a linear combination of (1, -1, 0), (0, 1, 1) and (3, -5, -2)

A: A linear combination is very significant in linear algebra. When some given vectors are multiplied…

Q: Find the equation of the cubic that best fits the given points: (-3, 1), (0, -1), (2, 5), (4, 2),…

A: X Y -3 1 0 -1 2 5 4 2 5 0