Find the center and the radius of the circle with the equation x2+12x+y2+6y−76=0 Enter the center as an ordered pair (x, y).

Q: Identify the surface defined by the following equation. 2x-y²-z² =0

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Q: At what point does the normal to y = 2 + 2x + 2x² at (1,6) intersect the parabola a second time?

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Q: Find the area of the surface formed by revolving the portion in the first quadrant of the graph of…

A: Rearrange the given equation to find y in terms of x and thus f(x). Plot the curve and find the…

Q: x^2+y^2−16x+14y+ 97= 0 is the equation of a circle with center (h,k) and radius r for: h= and k=…

A: Solution is done in step 2

Q: Find the points on the surface y2 36 + xz that are closest to the origin. (х, у, 2) (smaller…

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Q: Suppose XY has coordinates X( -2, 5) and Y(3, -9). What are the coordinates for the midpoint of XY?

A: To find the Midpoint of the line.

Q: Calculate the equation of the circle that passes through the point (0, -3), whose radius is V5 and…

A: we know that equation of circle (x-h)2+(y-k)2=r2  Here radius of circle is 5 ,here circle passing…

Q: Find an equation of the circle with center at (– 5, – 5) that is tangent to the y-axis in the form…

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Q: Find the center and the radius of circle. x2+y2-8x+6y+21=0

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Q: Find the center C(h,k) and radius (a) :of the circle 9. x² + y² – 4x 4 0 =

A: Write in standard form

Q: Find an equation of the line containing the centers of thetwo circles x2 + y2 - 4x + 6y + 4 = 0 and…

A: The given circle equations are x2+y2-4x+6y+4=0    and   x2+y2+6x+4y+9=0. Compare the above circle…

Q: What is the equation of a circle that passes through the vertex and the points of latus rectum of…

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Q: Find for the equation of a circle with center at (-1, 4) and passes through the point (3, 2).…

A: Standard equation of a circle with center at A=(−1,4) passing throught the point B =(3,2)   Find…

Q: Find the points on the surface x² −yz = 5 that are closest to the origin.

A: Let the point P be (x,y,z). The distance between the point P and origin is given by the formula…

Q: Find the points on the surface xy2z3=2 that are closest to the origin.

A: Given, xy2z3=2We have to find the point on the given surface that are closest to origin.let the…

Q: x + y? – 14x + 6y + 54 = 0 is the equation of a circle with center (h, k) and radius r for: %3D h =…

A: Lets find radius r  and  center(h,k).

Q: 10. Find the center and radius of the circle whose equation is x² + 5x + y² – 6y + 12 = 0. A.…

A: To find The center and radius of the circle.

Q: when the center of a circle is at the origin, the equation to be used is when the center of a circle…

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Q: By differentiating implicitly, find the slope of the hyperboloid x +y? - z = 1 in the r-direction at…

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Q: Find equations for two lines through the origin that are tangent to the ellipse x - 8x +y +5 = 0. YI…

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Q: 2* + y – 10x+ 18y – 90 = 0 is the equation of a circle with center (h, k) and radius r for:

A: The given equation of a circle x2+y2-10x+18y-90=0 Completing the squares…

Q: Find the center and the radius of the sphere. 2 + y2 + z2 + 4x + 5z = 0

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Q: Find the equation of the circle with center at the origin and radius v11 * X^2+y^2=v11 X^2+y^2= 11 O…

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Q: Find the point(s) of intersection of the parabola y =x2+ 2 andthe line y = x + 4.

A: The given functions are y=x2+2   and   y=x+4

Q: 3x +3y- 24x 30y + 96 = 0 is the equation of a circle with center (h, k) | and radius r for: h = and…

A: Given equation 3x2+3y2-24x-30y+96=0 The objective is to find the center and radius of a circle.

Q: A circle whose equation is x2 + y2 + 4x + 6y – 23 = 0 has its center at ______.

A: Given equation,

Q: Identify the surfaces represented by the equations and sketch their graphs. 1. x2 + 4y2 + 9z2 36

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Q: Find the center and radius of the sphere. * + + 5z +x+y+z= 4 5x +

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Q: 4. What is the equation of a circle with radius 3 and center (3, 0)? A. x2 + y2 – 6x = 0 B. x2 + y?…

A: equation of the circle with radius 3 and center (3, 0) :(x-3)2+(y-0)2 = 32

Q: A circle with radius 2 contains the point (1,-4). Which of the following equations best describes…

A: The given point is 1, -4The radius is 2

Q: |xy dA, D is enclosed by the quarter-circle 20. y - 1 - x² , x > 0, and the axes

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Q: Find the point on the surface x2 − 2xy + y2 − x + y = 0 closest to the point (3, 4, −5).

A: Consider the provided surface

Q: Find an equation of the line containing the centers of the two circles x2 + y2 + 2x + 2y + 1 = 0 and…

A: Given,

Q: 2x +2y +4 + 8y + 2 = 0 is the equation of a circle with center (h, k) and radius r for: h and and

A:

Q: 1. The equation of the circle is x² – 2x + y² +6y =-6, its center is and th radius is

A: 1. The equation of the circle is,  x² - 2x + y² + 6y = -6 So, (x² - 2x + 1) + (y² + 6y + 9) = 1+9-6…

Q: Find the equation of the circle with center (–1, 4) and radius of 3. [A] (x+1)² + (y+4)² = 9 [B]…

A: A circle is the locus of points in two-dimensional space which are equidistant from a fixed point.…

Q: Find the lines tangent to the ellipse x2/4 + y2/9=1 that contain the point (4, 0).

A: We at first consider the equation of tangent  to x2/4 + y2 /9=1 with slope m. Then we find the value…

Q: Find the equation of the circle with center 2+31 and radius4 units. (A) (x-2) +(y-3) =4 (C) (x-2)…

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Q: ^2+84x-24y

A: Given Ellipse: 21x2-4y2+84x-24y=36This equation can be re-written as-21(x2+4x)-4(y2+6y)=36 To find…

Q: Describe the surface given by the equation, and find xy-trace, xz- trace, and yz-trace. 16x2 + 16y?…

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Q: Find the points on the surface y2 = 64 + xz that are closest to the origin. %3D (х, у, 2) 3 (smaller…

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Q: Find for the equation of a circle with center at (-1, 4) and passes through the point (3. 2).…

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Q: Identify the surface with equation o = = 7

A: Spherical coordinates: The point Pρ, θ, φ represents a point in the spherical coordinates, where ρ…

Q: What are the coordinates of the center of the curve x2 + y2 – 2x – 4y – 31 = 0?

A: Given, To find coordinates of center for the curve x2 + y2 – 2x – 4y – 31 = 0?

Q: Find the equation of the family of circles whose center is at the y-axis. A. y "+ 3y + 7 = 0 В. ху "…

A: Please refer the attached image for complete solution.

Q: What is the center of X x² + y² – 30x + 221 = 0? Show all work for full credit.

A: Topic = Geometry

Q: ont 9. x2 + y2 – 2x + 10y +1 = 0 10. x2 + y2 -6y - 4 0

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Q: Find equations for two lines through the origin that are tangent to the ellipse x – 4.x + y² + 3 =…

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Q: 2x + 2y + 16x + 4y+ 26 = 0 is the equation of a circle with center (h, k) and radius r for: h = and…

A: We will find  the center of the circle (h,k )and radius (r) in the following step.

Q: 2. Write the equation of the circle with Center (-1, – 8) and Radius : V7 x2 + 2x + y? + 16y + 58 =…

A: Topic-analytic geometry