Find the point P on the parabola y = x2 closest to the point (57, 0). (х, у) %3D ]-«

Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: Given:    z = x2 + y2  Point: ( 5, 0, 0 )

Q: 25 at the point ( 1, -1, 2 ).

A: Given that : The surface  8x2+y2+4z2 = 25 , point = ( 1, -1, 2 ).

Q: Find an equation of the tangent plane to the surface at the given point. x² + y² – 9z2 = 4, (-2, -3,…

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Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 ≤ t ≤ 2π, closest to the point (3/4, 0).…

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Q: The slope of the tangent line to the parabola y = 2a2 + 2a + 6 at the point ( – 2, 10) is: The…

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Q: A heat-seeking particle is located at the point (2, −3) on a metal plate whose temperature at (x, y)…

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Q: 5. What is the maximum vertical distance between the line y = x + 2 and the parabola y = x² for – 1…

A: The given equations are, y = x + 2       ....(1)  y = x2            ....(2) To find the maximum…

Q: The tangent of the parabola x = y² + y + 1 at the point (1,0) is

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Q: Find the point (xo, yo) on the graph of y = x' + 9x² + 6x – 3, at which the slope of the tangent…

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Q: The curve y = ax² + bx + c passes through the point (2, 28) and is tangent to the line y = 4x at the…

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Q: Solve 3x – 6 ≥ 0 graphically intwo dimensional plane.

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Q: Find the area of the segment of a sphere formed by revolving the graph of y = √25-x2,0 sxs 4, about…

A: Given y=25-x2, 0≤x≤4 A sphere is a geometrical object that is a three-dimensional analogue to a…

Q: Find the parabola with equation y = ax2 + bx whose tangent line at (1, –1) has equation y = 3x – 4.…

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Q: What is the shortest distance from the surface xy + 15x + z2 = 204 to the origin? distance =

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Q: Tangent to the parabola z = x² + 3y² , x = 1 , at point ( 1, 2, 13

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2, 5/6). Sketch the…

A: To find the trajectories of the hyperbola write dydx by dxdy  and solve the system.

Q: Find an equation of the tangent plane to the surface 9x2 + y2 + 4z2 = 25, at the given point (0, −3,…

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: ` What is the shortest distance from the surface xy + 9x + z² = 76 to the origin? distance =

A: z2+9x+xy=76z2=76-9x-xy   ---- Eq 1Let P(x,y,z) be a point on the given surface. We know that…

Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 <=t<= 2pai closest to the point (3/4,…

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Q: Q1/ plot x2-y2=z (Elliptic paraboloid) in 3D.

A: Topic:- plot in 3-D

Q: Find the points on the hyperbolic cylinder x2 - z2 -1 = 0 that are closest to the origin. please…

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Q: Find the point (xo, yo) on the graph of y = x + 3x² + 4x – 5, at which the slope of the tangent line…

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Q: 4. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch the…

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Q: Where does the normal line to the parabola y= x- x2 at  the point (1, 0) intersect the parabola a…

A: Normal to a curve is a line which is perpendicular to the curve at its point of intersection with…

Q: dy Use the method of isoclines to draw several solution curves for the equation dr

A: First integrate the function using variable separation method and find y as function of x  Then draw…

Q: Find the equations of the tangent line and normal line to the parabola y=2x2 at the point (2,8).

A: We find dy/dx at x=2 to find the slope of the tangent  Then we use the point-slope formula to find…

Q: Find the point (x0, yo) on the graph of y = x + 9x² + 8x – 5, at which the slope of the tangent line…

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Q: find the point p on the line y=5x that is closest to the point (78,0). what is the least distance…

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Q: -axis. 5. Evaluate dV, where E is the solid tetrahedron with vertices at (0,0, 0), (2, 0, 0),…

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Q: Find the point on the parabola y = x^2 closest to the point (−3, 0)? and give the minimal distance?

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Q: Find the minimum distance from the cone z = 2x2 + y2 to the point (-6, 4, 0).

A: To find the minimum distance first write distance function. Which is the square distance from  .

Q: Find the point (xo, yo) on the graph of y = x + 3x2 + 5x – 3, at which the slope of the tangent line…

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Q: 2-g(%,y)%3D플-플 * at (VT ,1)

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Q: Make the cubic y = ax3+bx2+cx+d pass through the points (0,-6), (1,-2) and be tangent to the line…

A: This is the simple question based on algebra and derivative which could be solved using the basic…

Q: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for -1 <x<…

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Q: Find the points on the hyperbolic cylinder x2 - z2 -1 =0 that are closest to the origin. please…

A: The parametric equation of hyperbolic cylinderx2-z2-1=0 is , x=cos hθ                          y=y…

Q: How close does the semicircle y = V16 – x² come to the point (1, v5)? |

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Q: 3. Find how many roots the equation 2z4 – 323 + 3z² – z + 1 = 0 - - has in the right half-plane Rez…

A: Given: 2z4-3z3+3z2-z+1=0

Q: Find an equation of the tangent plane to the surface at the given point. x² + y²5z² = 29, (-3, -5,…

A: Solution of given question is written in below steps.

Q: The semi-hyperbola H(X)=(sqrt(x^2-1)) is continous at which x interval?

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Q: The 50 g bullet travelling at 100 ms-1 strikes the 2 kg block centrally and is embedded within it.…

A: Please check step 2 for the solution.

Q: What is the average distance between the parabola y = 7x(16-x) and the x-axis on the interval…

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Q: Find the slope of the tangent to the curve of intersection of the survace 3z =√36 – 9x² – 4y² and…

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Q: y 1-

A: The solution is given below in the next step:

Q: What is the maximum vertical distance between the line y = x + 29 and the parabola y = x² over the…

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Q: Find the point (xo, yo) on the graph of y = x' + 9x² + 7x – 5, at which the slope of the tangent…

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Q: The maximum vertical distance between the parabola y = 3-z and the line y = 3x+2 on the interval…

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Q: Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

A: This is a problem of geometry. We will calculate slope of x, y and z at given point and general…

Q: Find the orthogonal trajectories of the families of Parabolas y a + 8az + 16a, which passes through…

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