A surface in space is defined by the equation -4x? + 16y- 8z2 = 0. Which one of these is true? O The surface is a cylinder with an elliptical generating curve. The surface is a cone whose traces parallel to the xz-plane are ellipses. The surface is a cone whose traces parallel to the xy-plane are parabolas. O The surface is a hyperboloid of one sheet.

Q: Which of the following equations represents a parabola with vertex (5,2) and directrix y = - 2? (А)…

A: Let's find equation of parabola.

Q: 5x² - 7y² - 5z² = 1

A: The equation is

Q: Identify the quadratic surface of the equation 6x? + 3y? + 222 + 24x – 6y – 12z + 39 = 0 Choose an…

A: Given, 6x ^ 2 + 3y ^ 2 + 2z ^ 2 + 24x - 6y - 12z + 39 = 0

Q: What is the equation of the parabola containing the points (0, 5), (–1,9), and (2, 3)? O y = r-z+5 O…

A: The standard form of a parabola is y=ax2+bx+c. The required parabola passes through the 3 points are…

Q: Find an equation of the parabola with vertex , 34 and directrix =y2 .

A: It is given that the vertex of the parabola is (3,4), where h = 3 and k = 4 and the directrix is y =…

Q: Which equation represents the parabola graphed on the coordinate plane below? Ay-x-8²-6 А directrix…

A: Vertex form of parabola with vertex h,k⇒y=ax-h2+k

Q: Find an equation of the parabola with vertex (5,-5) and directrix y=-3   .

A:

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: Sketch parabola y = x2 – 10x + 16 by plotting a few points to left and right of the vertex. (Find…

A: Given parabola y=x2-10x+16                  ....(1)

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 length of the latus rectum of the ellipse defined by 25x? + 9y? - 300x - 144 y + 1251 -0 3.0 3.2…

A:

Q: Express the general form to its standard form and locate the center, vertices, covertices and foci…

A: equation 4x2 - y2 - 32x - 4y + 24 = 0

Q: Determine the ends of the minor axis of the following ellipse: .(x+3)² (y+4)² = 1 16 25 O (-7, -4)…

A: Use ellipse concept

Q: Which equation represents a parabola with focus (2, 6) and directrix y = 2? A. y+4=(x-2)² 10 B.…

A:

Q: parabola passes through (15,0) (25,30) (35,80). find the equation of the parabola in the form…

A: Given: A parabola passes through (15,0) (25,30) (35,80). To find:- The equation of the parabola in…

Q: (z – #1)² (y – yn)² 1 to find the y-values to the nearest integer from the given z and y-values in…

A: We have to find out y value

Q: Identify the quadric surface for the equation y² - x² = 16. a parabolic cylinder a hyperbolic…

A:

Q: 13. What are the center and radius of the circle (x−7)^2+(y+6)^2=4 A.C:  (7,-6); r= 16  B.C:…

A:

Q: A parabola has a focus of (4,5) and a directrix of y=1. Write its equation in the form of y-k =…

A:

Q: State whether the equation 4x² = 5z + 4y² defines an elliptic cone. a hyperboloid of one sheet. a…

A:

Q: Find an equation of the sphere whose diameter is the line segment having endpoints at (6,2, –5)

A: To find the equation of sphere.