. Find the point on the parabola y = x² closest to (6,3). newor: The noint is (24)

Q: dr if F= and C is a piece of the parabola y=4-x² from the point (–1,3) to the point (2,0).

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Q: Let P and Q be distinct points on the parabola y = 2r such that a circle with PQ as diameter passes…

A: The given equation of parabola y2=2x Let P and Q be points on the parabola  Parametric coordinates…

Q: Find the length of the arc of the parabola x2 = 4y from x = -2 to x = 2. А. 4.3 В. 4.6 С. 4.9 D. 5.2

A: we have to find the length of the arc of the parabola x2=4y from x=-2 to x=2

Q: Find the greatest and smallest values that the function f(x, y) = 4x+5y takes on the circle x2 + y?…

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Q: Show that the center of the osculating circle for the parabola y = x2 at the point (a, a2) is…

A: We need to show that the centre of the osculating circle for the parabola y = x2 at the point (a,…

Q: Find the maximum and minimum values of the function ƒ(x, y) = 3x + 4y on the circle x2 + y2 = 1.

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Q: The area of the triangle formed by the tangent and the normal to the parabola y = 4ax both drawn at…

A: Given  the parabola y² = 4ax both drawn at the same end of the latus rectum and the axis of the…

Q: Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8. 1 O f(x) -(x –…

A: Given query is to find the equation of parabola.

Q: Find the points on the surface x² + y² + z² = 4 farthest from the point (1,–1,1), 2 %D

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Q: Q3) Using the property of Re z and Im z to show that the hyperbola x2 – y? = 1 can be written as: z2…

A: Given that: Equation of hyperbola is-             x2-y2=1

Q: A] Find the length of the arc of the semi-cubical parabola y2 x (1,1) and (5,5V5). 8250 between the…

A: Solution:Given        y2=x3    between the points (1,1) and (5,55)To find the Arc…

Q: 13. The parabola y = x2 + x + 1 opens: A. To the right %3D B. To the left C. Upward D. Downwarč

A: y=x2+x+1 here parabola is in the form of y=ax2+bx+c which means it can be open up or down…

Q: 2. Evaluate dy, where C is the part of the parabola y = x² from (1, 1) to (2, 4).

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Q: Find the exact length of the curve. y2 - 16(x + 4)3, Osxs 2, y > 0

A: The given equation of the curve is y2=16x+43, 0≤x≤2, y>0. The graph of this curve in the interval…

Q: Find b and c, given that the parabola y = x2 + bx + c passes through (0, 5) and (3, 23).

A: (0,5) means when x=0 then y=5. similarly, (3,23) means when x=3 , then y=23.

Q: Find the exact length of the curve. y = x3/2, osxs 6 3

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Q: Show that the number 4p is the width of the parabola x2 = 4py (p>0) at the focus by showing that…

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Q: 9) Find the point on the parabola y = 10-x² closest to the point (0, 5.5).

A: Given question:- Find the point on parabola y= 10-x2 closest to point (0,5.5)

Q: Let F(r, y) = (x + 1)7, and let C be the portion of the parabola y = x² that starts at (0,0) and…

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Q: Find the coordinates of the point on the parabola y = x² which is closest to the point (3, 0).

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Q: find the points on the parabola y=x^2 closest to the point (0,1)

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Q: on the hyperbola xy = 1. %3D Which of the followings is TRUE for f(x, y) = x² + y? %3D Litfen birini…

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Q: Sketch the graph of the cylinder given by 4x2 + 9y2 = 36. show solution

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Q: Find the area of the segment cut off from the parabola x2 = 8y by the line x- 2y + 8 = U. %3D

A: Introduction ::

Q: Find the tangent lines as directed. To the parabola y=6x-3 perpendicular to the line x+3y=7

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Q: a. Find the length of the arc of the semicubical parabola ay=x' , from x= to x= 5a.

A: Arc length of the curve

Q: Find the point on the parabola y = x³ that is closest to the point (1, 2) with two digits accuracy…

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Q: Find the shorted distance from the point A(2, to a point on the parabola y = x². And find the point…

A: Let (x,y) = (x,x2) point on the parabola is closest to A Distance between (2 , 1/2) and (x,x2) is:…

Q: 5.Find the point on the parabola x? = 4y nearest to (0,4).

A: Given:      x2 = 4y    Point : ( 0 , 4 )

Q: 4. Fit a second degree parabola y = a + bx + cx? to the following data 2. 8. 10 y 3.07 12.85 31.47…

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Q: Find the length of the arc of the parabola y²=4x from the vertex to a point where x=4.

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Q: Find the point(s) on the parabola x =y closest to the point (0,3)

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Q: drawn from the point A(2,10) on the parabola y = x^2 + bx + c Since the tangent is parallel to y =…

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Q: Find the point on the parabola x = t, y = t2, -∞ < t < ∞ closest to the point (2, 1/2).

A: Given Data The first equation is x=t. The second equation is y=t². The point is (2,1/2).…

Q: Find the length of the parabola given by c(t) = (t, t2) for 0 ≤ t ≤ 1.

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Q: If a parabola defined by f(x)=2−x^2 is inscribed under an equilateral triangle ABC, so that the…

A: Given data:     The given equation of parabola is: f(x)=2-x2.     The below figure represents the…

Q: Evaluate x° ds where C is the part of the parabola y = x² from (0,0) to (2, 4).

A: Form the double integral and set the limits than integrate with respect to y and x.

Q: Find a parametrization of the osculating circle for the parabola y= X sequar when x=1

A: The given equation of parabola is y = x2.We are asked to find the equation of osculating circle for…

Q: The region in the first quadrant bounded above by the parabola y = x ^ 2 below by the x -axis, and…

A: Follow the steps.

Q: Evaluate (x - iy) dz along (a) the parabola y = 2r? from (1, 2) to (2, 8),

A: In the given problem we have to evaluate  ∫C(x2-iy2)dz  along the parabola  y=2x2 from (1,2) to (2,…

Q: Let F(x, y) = (x + 1)j, and let C be the portion of the parabola y = x² that starts at (0,0) and…

A: The integral ∫CF⇀.dr⇀ is positive. From the graph the angle between direction of F⇀ and dr⇀  is…

Q: Find the x intercept(s) and the coordinates of the vertex for the parabola y = x^2 – 2x + 1. If…

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Q: Which of the following points do not lie on any tangent line of the parabola y = x2 + 2? (2,6) O…

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Q: The area of the region to the left of the parabola x=2y^2, to the right of the y-axis, and between…

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Q: Fnd the x uterceptis) and the coordinates of the vertex for the parabola y=x+10x+25. If there is…

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Q: 1. Find the point on the parabola y = 3 – x² that is closest to the point (6, 0).

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

A: Given the equation of parabolay=x2         ........(1)

Q: The line x=C where C70 intersects the cubic y= 2x3 + 3x²-9 a七 the point P and parabola y = 4x+ 4x +5…

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Q: Compute y ds over the part of the parabola y =2Px, for P > 0 starting at (0,0) at (2P,2P).

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Q: 33) Find the points of intersection between the line x - y - 2 = 0 and the parabola y = 4 - x 2.

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