planes and in the plane with equation 1 (a, b,c > 0). The х %3D volume of the tetrahedron is given by V = kabc. Find the minimum value of V among all planes passing through the point P = (1, 1, 1). C = (0, 0, c) •P B = (0, b, 0) A = (a, 0, 0) FIGURE 19

Q: What are the vertices and foci of the hyperbola (x - 9)2/25 - (y + 6)2/144 = 1 Show all work.

A: We have to find the vertices and foci of the given hyperbola.

Q: Write the equation of Spheres with radius R.

A:

Q: Write the coordinates for the center of the hyperbola: A/ (x-2) (y + 1)² 64 36

A: given  (x-2)236-(y+1)264=1standard form of hyperbola is  (x-h)2a2-(y-k)2b2=1hwer centre is  (h,k)

Q: the ellipse with 4) Write the the center at (o,o), the vertex at Cos-5) and the distance between the…

A: Given center at (0,0), vertex at (0,-5) the distance between focus and vertex is equal to 2 ⇒focus…

Q: Explain why it is not possible for a hyperbola to have foci at (0, -2) and (0, 2) and vertices at…

A: The standard form of the equation of a hyperbola with center (0,0) and transverse axis on the y-axis…

Q: The cross section of a cooling tower of a nuclear reactor is in the shape of a hyperbola and can be…

A:

Q: Rewrite to standard form by completing the square and identify the conic: a) x² +16y² - 10x +96y +…

A:

Q: Graph the points (3, 45 degree), (2, -4p/3), (-4, p/3), and (25, -210 degree )on a polar coordinate…

A: The given points are (3, 45 degree), (2, -4p/3), (-4, p/3), and (25, -210 degree ) Plot the above…

Q: 7. FIND THE EQUATION FOR EACH CONIC: ELLIPSE, = (0,-4) VERTEX = (8,-4

A:

Q: Express the conics in polar coordinates.

A:

Q: Find the equations of the following conics and quadric surfaces relative to principal axes. 3x² +…

A: The answer provided below has been developed in a clear step by step manner

Q: Write the equation of the parabola with vertex at (-9, 0) and directrix at x = -10 a) + 9 1,2 49 b)…

A: Given

Q: It is true that the vertex is halfway between tje focus and the directrix on the principal axis

A: Yes, the vertex is halfway between focus and the directrix on the principle axis

Q: State the polar Equation of a Conic Section.

A: Polar equations of conic sections:  If the directrix is a distance d away, then the polar form of a…

Q: Write the equation for the sphere of radius 1 centered at the prigin in the each of the following…

A: The general equation of a sphere in cartesian coordinates is: x-a2+y-b2+z-c2 = r2 Here, r is the…

Q: 6) Complete the square on the ellipse 1622 + 25y? – 32.x + 100y – 284 = 0 to write it in standard…

A: Completing the square on the ellipse 16x2+25y2-32x+100y=284 16x2-32x+25y2+100y=284…

Q: 1) Find the focus, vertex, direction of the parabola and directrix of the following equations: a) y…

A: To find the Focus, vertex , direction of the parabola and directrix a) y2=4x Direction of parabola :…

Q: 3. Equation: Center: Vertices: Co-Vertices: Foci:

A:

Q: What is the equation of the standard hyperbola with vertices at(0, ±a) and foci at (0, ±c)?

A: Given-  Hyperbola with vertices at (0, ±a) and foci at (0, ±c). To find- The standard equation of…

Q: entify the coni

A: Given,           x2+16y2-160y+384=0

Q: Given the equation of a hyperbola, find each of the following:  a) the center; b) the vertices;  and…

A:

Q: Explain why the dots in Figure 23 lie on a parabola. Where are the focus and directrix located? y=…

A: