nts, in a line, or in a circle? sphere intersects the xz-plane ? sphere intersects the yz-plane ?

Q: Describe the yz-intercept of the sphere with the equation x2 + y2+z2 - 2x+ 10z +5 = 0

A: The given equation of sphere is: x2+y2+z2-2x+10z+5=0

Q: . Use the method of completing the square to write the following equation in standard form and…

A:

Q: Suppose a and b are positive numbers. Sketch the parabolas y2 = 4a2 - 4ax      and         y2 = 4b2…

A:

Q: sketch y+3x =9 in two dimensional and three dimensional space

A: sketch y+3x =9 in two dimensional and three dimensional space

Q: By completing the square, put the equation 2 – 64y tử + 42 – 16z = –68 Into the standard form…

A:

Q: Find the equation of the sphere having the circle x +y+ z2 = 9, x- 2y+ 2z = 5 as a great circle.

A: The solution is below.

Q: Consider the paraboloid given by the equation z = x^2 + y^2. Find the coordinates of the vertex and…

A: A paraboloid is a quadric surface that has exactly one axis of symmetry and no center. The given…

Q: Write the equation of a sphere that has a center at C(2, 5,-3) and contains points D(4, 1, 1) on the…

A: Given Data: The centre of the sphere is: C(h, j, l)=C(2, 5, -3) The point at the edge of the sphere…

Q: Determine the surface with the equation 2x2-3y2-4z2-12x-6y-21=0

A: We have to determine the surface with the equation 2x2-3y2-4z2-12x-6y-21=0.

Q: A quadratic surface has the equation x2+2y2+2z2+2yz = 1. Write the equation in standard form.…

A: To write the quadratic surface equation \( x^2 + 2y^2 + 2z^2 + 2yz = 1 \) in standard form and…

Q: The graph of x2+y2+z2-14y=0 is a sphere. what are the center and radius of the sphere?

A: Given    Equation of sphere  x2+y2+z2-14y=0To calculate:-     Center  and  radius  of the sphere.

Q: Find the center and radius of a sphere given by equation 3x +3y² +3z? =10+6y+12z.

A: We have to find

Q: Complete the square method: Show all your work! Put x² + y² 10x + 6y 15 = 0 in center radius form.…

A:

Q: Convert the following. form to general form of parabola a₁)(x-3) ²= 12 (1-4) 6.)(x-1)² = 8(4-3)…

A:

Q: Which quadric surfaces have both hyperbolas and parabolas as traces?

A: Consider the given: The intersection of a three-dimensional surface and a plane is called a trace.…

Q: The focus of the parabola defined by the equation x2 = 20 y is (4, 5) (0, 0) O Option 1 O Option 2…

A:

Q: Find the equation of a circle in standard form whose center is at (-4,3) and radius v5 * O…

A:

Q: Write the quadratic surface x2-y2+4z2+2x+4y+1=0 in standard form.

A:

Q: (2x-y (22) + (x+2)- 3 = 1.

A: Given: Equation of the ellipse: Objective: To find the area of the interior of the ellipse.

Q: Find the points of intersection between the line 4y - 3x + 12 = 0 and the ellipse 9x 2 + 16y 2 =…

A: The line 4y-3x+12=0 And the Ellipse 9x2+16y2=144 We need to find the intersection point of the line…

Q: Find the center of the sphere x² + y? + z? + 4x – 8z + 19 =

A: To find the center of the equation from the given equation.

Q: Arrange the parabolas represented by the equations according to the positions of their foci on the…

A: The standard form of a parabola is  (x – h)2 = a(y – k) where (h, k) is the vertex.

Q: The equation x² + 14x + y² – 8y +z2 +10z = – 65 represents a sphere whose center is (-7,4, – 5) |

A:

Q: Prove that a·a= = |a|2, where a is a vector with n components

A:

Q: Determine whether the equation x² + y² + 2² − 8x + 4y + 2z -4 = 0 is a sphere, a point, or a null…

A: