Astronomers discover a new comet. They study the path and discover that it can be modeled by a branch of a hyperbola with equation 4x² – 40x – 25 y = 0. a) Rewrite this equation in standard form and find the center of the hyperbola b) Astronomers also discover a pair of twin planets at the foci of the comet. Where are the planets located?

Q: The equation -y+3) 3D (x+ 6)² represents which conic section? a. circle c. hyperbola b. ellipse d.…

A: 1. The given equation is -65(y+3)=(x+6)2 2. The given equation is y29+x225=1

Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

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Q: 3) Foci: (-4, -8 + 4√2), (-4, −8 - 4√2) Endpoints of major axis: (-4, -2), (-4, -14)

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Q: The equation of the shown hyperbola is

A: Given, The graph of Hyperbola  We have to find the equation of hyperbola.

Q: Write the standard form equation for each ellipse described. Endpoints of axes are (4,0), (-4,0),…

A: Given, endpoints of axes are (4,0), (-4,0), (0,5), and (0,-5) We have to find the standard form…

Q: Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0,4),…

A: To find the standard equation of ellipse that satisfies the below condition. Foci: 0,−4,0,4;…

Q: Write the standard form equation for each ellipse described. Foci (0,8) and (0,8) and vertices…

A: The objective is to write the standard form equation for each ellipse. Given foci 0,8 and 0,-8,…

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: The graphs of the equations (image) are called conjugate hyperbolas. Sketch the graphs of both…

A: Consider the given equation of hyperbolas.

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

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Q: 7. Convert the equati- conic section the e center. If it is a par 4x² - y² + 32x+6y +

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Q: Find the vertices and locate the foci of the hyperbola with the given equation. Then graph the…

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Q: 10) Center at (-8, -1) Transverse axis is horizontal and 14 units long Conjugate axis is 8 units…

A: we  will find the required.

Q: Question: Find an equation of the hyperbola that has vertices (0, ±3) and foci (0, ±4).

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