In each part, find an equation of the sphere with center (1, – 7, –8) and satisfying the given condition. (a) Tangent to the xy-plane. Equation: (b) Tangent to the xz-plane. Equation: (c) Tangent to the yz-plane. Equation:

Q: Show that the equation represents a sphere, and find its center and radius: 2x2+2y2+2z2=8x-24z+1

A: To show that the equation represents a sphere, and find its center and radius: 2x2+2y2+2z2=8x-24z+1

Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 1) and directrix…

A: Given that Focus of parabola is F0, 1. Directrix is y=-1. We have to prove that y=14x2 is the…

Q: Write the equation of the sphere in standard form. x2 + y2 + z2 + 12x - 4y + 4z + 35 = 0 Find its…

A:

Q: Find parametric equations for each of the following. The circle of radius 2, centered at (0, 3, 0)…

A: We should understand that y is going to be constant  and is going to be 3   Now since r = 2 [given]…

Q: Find the center and the radius of the sphere x + y² += - 4x+ y-6z+13=0 Center: Radius:

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Q: In each part, find an equation of the sphere with center (5, -6, –3) and satisfying the given…

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Q: Find the standard equation of the sphere with the given characteristics.

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Q: Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 42² = 4…

A: To find: Parametric equation of the Intersections of the curves  4x2+y2+4z2=4 and y2=x2+2z2.

Q: Complete the parametric equations for the line where the planes – 3x – 9y – 12z - 11x + 2y – 10z 33…

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Q: snip

A: Given statement: A                  is the set of points P in the plane such that the ratio of the…

Q: Find the equation of the sphere with the given conditions: (a) center at (1, – 2, – 4) and its…

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Q: Find the standard equation of the sphere with the given characteristi Center: (-1, -9, 7) Radius: 9…

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Q: Find the parametric form of (i) the circle x²+y² = p² (ii) the ellipse 2 y² =1 (ii) the straight…

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Q: Find the equation of the xy-trace of the sphere. (x – 2)? + (y + 4)² + (z – 6)? = 72 Sketch the…

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Q: For the ellipse b'x' + a'y a'b?, show that the equations of its tangents of slope m

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Q: Find a parametric form for the line through the point (8, –6, –3) and perpendicular to the plane 2x…

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Q: In each part, find an equation of the sphere with center (5, –8, –2) and satisfying the given…

A: Given  Centre of sphere is =(5,-8,-2)

Q: Find an equation for the sphere with center at (-7,8,0) and radius = 9 O x2 + y? O x2 + y2 + z- -…

A: We have to find

Q: In each part, find the standard equation of the sphere that satisfies the stated conditions. (a)…

A:

Q: Find parametric equations and a parameter interval for the motion of a particle starting at the…

A: Given,

Q: In each part, find an equation of the sphere with center (2, –3, –3) and satisfying the given…

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Q: Consider the curve in the xy plane defined by the equation 4y? – 22 – 8y – 6x = 21 Show that this…

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Q: Write the equation of the sphere in standard form. x2 + y2 + z2 + 8x - 4y + 4z + 15 = 0 Find its…

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Q: Come up with a parametric description of the circle (x- 2)° +(y+4)* = 9. Make it so that the circle…

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Q: use the Discriminant Test to determine the type of the conic section (in each case, theequation is…

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Q: Find the equation of the sphere in standard form that satisfies the given conditions. center C(-1,…

A: Equation of sphere  standard form of sphere equation

Q: Find the point P of intersection between the line x(t) = (-3,-2, 1) + t (1, 1, -3) and the plane 4z…

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Q: Find a parameterization of the line formed by the intersection of the following planes: 1:2x-y+3z 1…

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Q: Find an equation for the sphere with a) center at the origin and radius length r = b) center (2, –…

A: Let the coordinates of centre of sphere be a, b, c and radius be r.

Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 1) and directrix…

A: Given that Focus of the parabola is F0, 1 and Directrix is y=-1 We have to prove that y=14x2 is the…

Q: A sphere has center in the first octant and is tangent to each of the three coordinate planes. The…

A: If the radius is r, then centre is (r, r, r) Given that distance between centre and origin is 3-3…

Q: Find parametric equations, in terms of t, of the line passing through (2, 2, 12) and parallel to the…

A: Given: The line is passing through 2,2,12. Also, it is parallel to the line: x=5-9ty=2z=4+t The…

Q: In each part, find an equation of the sphere with center (2, −1, −3) and satisfying the given…

A: Given that: Centre of sphere = (2, -1, -3)

Q: 2. Determine the orthogonal trajectory of the family of hyperbolas y² – 121x² = c. c. Sketch some of…

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Q: In each part, find an equation of the sphere with center (5, –8, –4) and satisfying the given…

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Q: Complete the parametric equations for the line where the planes 8x + 13y – z = 27 and 9x + 15y – 12z…

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Q: Is the set of all points in a plane, the difference of whose distances from two fixed points (the…

A: For the given statement

Q: Find the standard equation of the sphere with the given characteristics. Endpoints of a diameter:…

A: Given endpoints of a diameter of sphere is 2,1,3 and 1,3,-1. The standard equation of sphere is…

Q: Find the standard form of the equation of the sphere with the given characteristics. Endpoints of a…

A: The standard form of the equation of sphere is given by Where ( x0, y0, z0) is the center and r is…

Q: For Exercise, determine whether the transverse axis and foci of the hyperbola are on the x-axis or…

A: The general equation of the horizontal transverse axis hyperbola is given by,

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, –3, 5) Radius:…

A: Given that: Centre of the sphere, (h,k,g)= (-1, -3, 5) and radius, R=6

Q: Find parametric equations for the circle with center(h,k) and radius .

A: Find parametric equations for the circle with center(h,k) and radius r.

Q: Consider the Equation:  x2 + y2 + z2 + 8x - 6y + 2z + 17 = 0 1. Show that the equation represents…

A: x2 + y2 + z2 + 8x - 6y + 2z + 17 = 0

Q: Use the given information to answer the following questions. center (5, -2, 1), radius 9 (a) Find an…

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Q: Find the center and radius of the sphere with equation (x + 3)² + (y + 1)² + (z − 1)² = 64 Center:…

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Q: Find the center and the radius of the sphere. x^2+y^2+z^2-6x+3z=0

A:

Q: Find parametric equations for the segment joining the given points. (1, 3) and (3, 6) 0 sts1 c(t)…

A: Let p and q be the points (1,3) and (3,6) The parametric equation of the segment joining p and q is…

Q: Find the parametric equation of the line of intersection of the planes 2x+y-z=1 and x-2y+3z-9

A: First find cross product take normal vector useformula