Decide which of the following equations may represent a circular conic section? Determine the center-point and radius of the section. 5x2 + 6x + 5y – 25 = 0 7x3 + 7y2 – 4x + 6y – 40 = 0 2x2 – 2y2 + 3x + 8y – 99 = 0 x2 + y? – 6x + 4y = 0 x² + y? – 6x + 4y + 40 = 0 -

Q: Find the equation of a sphere if one of its diameters has endpoints: (-10, -12, -13) and (4, 2, 1).…

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Q: Express the following equation in standard form, identify the conic section, and state the locations…

A: Conic section

Q: Write the equation of the hyperbola 4x2 – 25y? + 8x + 250y – 721 = 0 in standard form (x – h)? (y –…

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Q: Match each equation to the conic section it creates. (x+5)² 25 a. + (y-2)² 4 b. 3x³ + 4y = 25 d. = 1…

A: a. The standard equation of a ellipse is (x+x0)2a2+(y+y0)2b2=1.So (x+5)225+(y-2)24=1  is equation of…

Q: Determine whether the equation is that of a circle, parabola, ellipse, hyperbola, or none of these.…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Select the correct answer. Which equation represents the hyperbola that has its foci farthest from…

A: we know that if distance between two foci are greater then distance between foci and center is also…

Q: Write the equation of the hyperbola 16x² - 9y² +96x - 72y - 144 = 0 in standard form Where: h = k= a…

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Q: State whether the equation x² + ()² + 6z² = 1 defines O a hyperboloid of two sheets. O a paraboloid…

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Q: 6. Find the center of the ellipse with equation 2x² + 3y² + 8x + 6y - 1 = 0 b. (2, -1) а. (2, 1) с.…

A: We will solve the problem.

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: Classify the conic first, and then conv equation to standard form

A: The equation of given conic is -2x2+5y2+24x-20y-102=0 ......................(1)             Compare…

Q: Find the equation of the hyperbola with vertices at (-4,2) and (0,2) and foci at (-5,2) and (1,2).…

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Q: 42 - 8r - 16,

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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: Find the equation of the hyperboloid shown in the figure, B Z where a = 8, b = 10, A = 32, B = 40, Z…

A: Answer given below.

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.