A. Transform each equation to center-radius form and determine its center and radius. 1. x² + y² +8x14y + 1 = 0 2. x² + y² - 2x + 12y - 12 = 0 3. x² + y² + 4x-5=0 4. x² + y²-6y + 5 = 0 5. 4x² + 4y²-56x + 8y +56= 0

Q: Write the equation of the parabola given by y? + 2y + 12x – 23 = 0 in standard form. %3D -

A: Given equation of parabola is y2 + 2y + 12x - 23 = 0

Q: Complete the square to express y= 3x – 10x – 5 in the form y=a(x-h)² +k. Then give the coordinates…

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Q: A quadratic surface has the equation x2+2y2+2z2+2yz = 1. Write the equation in standard form.…

A: To write the quadratic surface equation \( x^2 + 2y^2 + 2z^2 + 2yz = 1 \) in standard form and…

Q: Find the y-intercept (b=) of the line 8x+5y=20 *

A: Given line is: 8x+5y=20 For calculating the y intercept, put x=0 So,  8×0+5b=205b=20b=4 is the…

Q: Find the equation of the circle which passes through the points (1,-2),(4,-3) and  whose center…

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Q: menE C. Find the center and the radius of the following equation: 5. x + y -16x+8y+31=0 6. x* +y…

A: Given equation of circle now we have to find centre and radius of circle as shown below

Q: Identify the quadric with the given equation and give its equation in standard form   16x2 + 100y2 +…

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Q: Let P(-5, -3, -7) and Q(7, 11, 1) be two points in three dimensional space. Write an equation of the…

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Q: Find the equation of the parabola with V(-2,-3) and a directrex y=-7

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Q: Graph the equation x2/4+ y2/9 = 1, and give the centerand the endpoints of the major axis

A: Given equation x24+y29=1

Q: Y² – 16X² + 64X – 208 = 0

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Q: Find the equation of the sphere that has the line segment joining (-1,-8,-6) and (-1,2,-6) as a…

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Q: Write (in standard form) the equation of a circle with center C(-4, 3) and containing point P(-2, 6

A: To find the equation of circle

Q: Eliminate the parameter (NO SPACES). - x = 2t - 3 and y = 9 – 4t y =

A: given→⇒x=2t-3............(1)⇒y=9-4t.............(2)

Q: Write the equation 4x² - 25y²-2² - 100 = 0 in standard form. Draw a sketch of its graph and name the…

A: Please see the below pictures for detailed solution.

Q: Find the points of intersection between the line 4y - 3x + 12 = 0 and the ellipse 9x 2 + 16y 2 =…

A: The line 4y-3x+12=0 And the Ellipse 9x2+16y2=144 We need to find the intersection point of the line…

Q: V4-x² x2+y2 4-x² x²+y² xdzdydx + ædzdydx V1-x² 0,

A: The given integral is∫01∫1-x24-x2∫0x2+y2xdzdydx+∫12∫04-x2∫0x2+y2xdzdydxWe have to convert integral…

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 whether the equation x² + y² + 2² − 8x + 4y + 2z -4 = 0 is a sphere, a point, or a null…

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Q: Find the equation of the parabola, y = ax2+bx+c, that passes through the points (−1, 6), (1, 4),…

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