Find the equation of a circle in standard form whose center is at (-4,3) and radius v5 * O (x+4)^2+(y-3)^2=5 O (x+6)^2+(y-3)^2=25 O (x+4)^2+(y+6)^2=4 O (x-5)^2+(y-3)^2=5

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: Find the standard equation of the hyperbola. Two corners of auxiliary rectangle at (−4 ,−7) and (0…

A: Given: The two corners of the auxiliary rectangle of a hyperbola are at -4,-7 and 0,0 and transverse…

Q: Find the equation of the circle passing through the points A(2,1), B(0,5), C(-1,2) using LU…

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Q: Find the equation in rectangular coordinates of the quadric surfaceconsisting of the two cones φ =…

A: The relation between spherical and rectangular coordinates in polar form is given by the following…

Q: Suppose a and b are positive numbers. Sketch the parabolas y2 = 4a2 - 4ax      and         y2 = 4b2…

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Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

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Q: Find the equation of the line tangent to the hyperbola x + 2xy - y + x = 5 at the point (3,7)

A: Given,            x2+2xy -y2+x =5 and point (3,7)

Q: There is a parabola which has a minimum where the two lines 3x+6y-1=0 and 2x+ y-2=0 intersect. The…

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Q: Find the equation of the sphere having the circle x +y+ z2 = 9, x- 2y+ 2z = 5 as a great circle.

A: The solution is below.

Q: What is the length of the latus rectum of a parabola having its vertex at the origin and focus at…

A: The length of latus rectum of parabola = 4a

Q: A parabola of y=x^2 has been regraphed and now sits with each side plotted at (-3,5) and (3,5) and…

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Q: Find the points on the ellipse 4x + y² = 4 that are farthest away from the point (1, 0). (х, у) %3D…

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Q: Write the equation for the hyperbola with foci (1,-5), (9.-5) and conjugate axis of length 6. (x-…

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Q: Find the equation of a sphere whose center is on line 5y+2z=0=2x-3y and passes through point…

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Q: Any point on the parabola can be labeled (x, y), as shown. 4 3 2 (*, y) ¢ -6 -5 -4 -3 2 - 1 2 3 4 5…

A: According to figure equation of parabola in standered form X2=4bYnew equation of…

Q: Determine the orthogonal trajectories of the family of ellipses 16x² + 121y² = C. Sketch some of the…

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Q: Find the standard equation of the sphere that has the points (5, −2, 3) and                  (0, 4,…

A: we know that equation of sphere which has end points of diameter as x1,y1,z1 and x2,y2,z2 is given…

Q: What is the equation of the directrix of the parabola having a vertex at (6,0), passing through…

A: Given:- What is the equation of the directrix of the parabola having a vertex at (6,0), passing…

Q: Find the coordinates of the foci of the ellipse with vertices at (11,3) and (-15,3) and has minor…

A: To find the coordinates of the foci of the ellipse with vertices at 11, 3 and -15, 3 and has minor…

Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

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Q: Find the equation of the parabola with vertex (−3,1)(−3,1) and yy-intercept 22(or (0,2)(0,2)).

A: topic - equation of a parabola

Q: Determine the center-radius Form of the equation of the sphere whose- diameter has endpoints at (2,…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Use disk method and draw a graph. √(9-y^2 ),y=1,y=3,x=0 about the y-axis

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Q: what is the equation of a parabola with a vertex at (4, 8) and a directrix at y=5

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Q: What is the name of the surface defined by the equation x2 y

A: Given Equation is :                                  y=x24+z28y=2x2+z282x2+z2=8y   Since,…

Q: Find the equations of the osculating circles of the parabola y = 3(x – 2)2 at the points (2,0)

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Q: Sketch parabola y = x2 – 10x + 16 by plotting a few points to left and right of the vertex. (Find…

A: Given parabola y=x2-10x+16                  ....(1)

Q: Why are 9x^2-81y^2=0 and 9x^2-(z^2/4)=0 hyperbolas that pass through the origin and not lines that…

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Q: Find the length of the diameter of the ellipse 3x2+y2 +2x-6y=0. Which has a slope of 2.

A: Ellipse

Q: Find the minimum distance between the point (5,1) and the parabola y=-x2 ?.

A: Find the minimum distance between the point (5, 1) and the parabola y = -x2?

Q: Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (1, 0). (х, у) %3…

A: The distance between of two-points: - The length of the line segment connecting two places is the…

Q: Find an equation of the ellipse with foci at (-5,9) and (-5,-10) and whose major axis has length 22.…

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Q: ress 3x² + y² + 2z² + 6x – 4y

A: Given,            3x2+y2+2z2+6x-4y-12z+26=0

Q: Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (1, 0). (x, y) =…

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Q: Sketch the section of the surface at y 0. -6 -4 -2 6. -2 2 -6 -4 -6 -4 -2 -6 -4

A: The objective of the question is sketch the section of the surface at y=0.

Q: Write the equation for the hyperbola with foci (1,-s), (2.-s) and conjugate axis of length 6. (x-…

A: Please refer the attached image for complete solution.

Q: Identify and sketch manually the graph of the quadric surface 25x² -25y² -9z²-150x + 200 = 0.

A: Solution :-

Q: Determine the type of conics for each equation using the discriminant. 20. 5x2 + 2x + 3y - 5 = 0 21.…

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Q: Identify and sketch the graph of the quadratic surface 4x2-y2-z=1

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Q: 4x^2 + y^2 = 4 that are the farthest away from point (1,0)

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Q: Find the standard equation of the sphere with center (-2, 5, -3), and radius 5.

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Q: The length of the latus rectum of the ellipse defined by 25x2 +9y2 - 300x – 144 y + 1251 = 0 is 3.0…

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Q: Sketch the graph of -x + 9y² – 4z² = 36 and identify the surface. %3D

A: Given a function in terms of x, y and z. Here x and y are independent variables and z is a dependent…

Q: find the orthogonal trajectory of family of parabolas represented by the equation…

A: To find orthogonal trajectories of  y2=4ax.

Q: Suppose the axis of a parabola is parallel to the yy-axis and passing through the points (0,3),…

A: Given that, the axis of a parabola is parallel to the y-axis. Let the Vertex of the parabola (h, k)…

Q: Find the orthogonal trajectory for the family of parabolas with center at the origin and focion on…

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Q: Find the equation of the line tangent to (a) The parabola z = 2x² - 3y², y = 1 at the point (-2,1,5)…

A: Given: we have to find equation of tangent lines   equation of tangent line : y-y1=m(x-x1)

Q: Find the point(s) on the ellipse 4x² + y² = 4 that are farthest from the point (1,0).

A: We need to find the points on the ellipse that is farthest from the given point. According to first…