Match the equations of the surface with the graphs below. f1.² + 4y² +9z² = 1 d 2. - x2 + V 22 = 1 3.9x² + 4y² +22² = 1 4.x² - y² +2²=1 C A D B C 500 E

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: -8 -6 618

A: Parabola is a locus of points equidistant from the directrix or straight line and focus. The general…

Q: ine the graph of the paraboloid z=x2+9y2. Choose the correct graph of the equation.

A: Given the paraboloid equation is                           z=x2+9y2.

Q: Match the equation with the surface it defines.​ Also, identify the surface by type​ (paraboloid,…

A: z2-y2=4x

Q: Consider the parabola C: z-4 = -(x - 2)² on the rz-plane. 1. Find the center-radius form of the…

A:

Q: The surface of a mountain is modeled by the equation h(x, y) = 7500 – 0.001x2 - 0.004y2. A mountain…

A: Given the surface of a mountain is modeled by the equation h(x,y)=7500−0.001x2−0.004y2

Q: 12. Use vertex form to write the equation of the parabola. y= 3(x+2)° +2 y= 3(x- 2)° +2 y= 3(x- 2)°…

A: best and easiest way is one by one checking if the given option satisfy the given points (-2, 2) and…

Q: Complete the square to write the following equation in the standard form for a sphere. x²+y²…

A:

Q: Show, by completing the square, that the parabolay = ax2 + bx +c can be obtained from y = ax 2 by a…

A: The given equation of parabola is y=ax2+bx+c. Rewrite the above equation as follows.…

Q: What is the equation of a parabola that intersects the x-axis at points (-1, 0) and (3, 0)?   A. y…

A: Given that: A parabola intersects x-axis at (-1, 0) and (3, 0)

Q: Provide a hand-drawn sketch of S using the traces obtained in (a). Label all important points found…

A: As per the question we are given a 3d surface S defined as : 4x2 - (y-3)2 + 4z2 = 4 And we have to…

Q: Graph the surface of the following equation: y = 4x² - 4z²

A: The given equation is Sketch the graph of the given equation.

Q: 4. For each equation given below, write down the name of the surface it represents. The options are:…

A: We have to name the surface that each equation represents.First we will rewrite the equation and…

Q: What is the equation of the line that contains the vertices of the hyperbola (x + 4)² (y + 2)² -1? 9…

A: Finding the vertices

Q: Indicate whether the following equations define a straight line (L), a circle (C), an ellipse (but…

A: Concept of identifying the equation Circle for the equation of circle, both x and y are squared…

Q: What is the equation of the parabola in general form given its vertex at (-1,-5) and focus at…

A:

Q: Consider the following equation of a quadric surface. x²y² + 100 25 a. Find the intercepts with the…

A:

Q: Identify and sketch by hand the graph of the quadric surface 36x² − 9y² +162² +36y - 180 = 0. You…

A:

Q: 1. Which is the equation of a parabola that is concave down with a y-intercept of 5? 1. y -+ 5x +1…

A:

Q: Match the equation with the surface it defines. Identify the surface by type​ (paraboloid,…

A: Solution:

Q: Find the equation of sphere that passes through the point (-2, -8, -2) and centered at (8, 7, 8).…

A: To find the equation of the sphere that passes through the point -2, -8, -2 and centered at 8, 7, 8.

Q: x² + y² + (z – 2)² = 122

A:

Q: Write the equation of a circle with center (15. 12) and radius 3V6. x+ 15) • (y • 12 = 54 x - 15 +…

A:

Q: In which variable(s) should you complete the square to identify the surfacex = y2 + 2y + z2 - 4z +…

A: We have to determine which variable should we complete the square to identify the surface…