Find the equation of curve on which point P lies. The difference of the distance between P(xy) and the points (-2,1) and (8, 1) is 6.

Q: Find the length of the given curve. 4/3 3y2/3 X = -27 - 32

A: The arc length formula is L=∫ab1+f 'y2dy. Here, 3y43-3·y2332' =-1+64y2316y13. Thus, the length of…

Q: Find the exact length of the curve. y = 4 + 2x3/2, 0 < x < 1

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Q: For the curve given by x=t^2+t-2,y=t^3-2t-1, find the slope and concavity at the point (4 , 3).

A: In order to find the slope at point we need the value of t (the parameter) which is missing in the…

Q: At the given point, find the slope of the curve, the line that is tangent to the curve, or the line…

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Q: Suppose a curve is defined by the equation 16(x² + y²) = 45. Show that if you translate the curve to…

A: we have to translate the curve.

Q: The curve's equation is given by x* + y4 = x² + y?

A: Here is the solution of the given problem.

Q: Consider the curve y = 3x3, The sketch of the portion of this curve between x = - 1 and x = 8 is…

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Q: Find the exact length of the curve. y = 4 + 6x3/2, 0 < x < 1

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Q: given curve about the x-axis. 1. y = 7x, 0 < x <1

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

Q: find equations for the lines that are tangent,and the lines that are normal, to the curve at the…

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Q: Find the slopes and equations of the lines tangent to y = f(x) at the given point.

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Q: Given the curve y = x3 + 3x, at what point is y' = y'' ?

A: As we know that, The Power law: ddxxn=nxn-1 The sum/difference rule: f±g'=f'±g'   Given: y=x3+3x And…

Q: The x coordinate of the point of intersection between the two curves y = el4a and y = 1 is

A: Equate both equation

Q: Find the distance from the point Q to the line ℓ. Q = (2, 2), ℓ with equation [x y] = [-1 3] + t [1…

A: GIVEN: Q = (2,2)               xy = -13 + t 1-1

Q: Find the coordinates of the point in the curve y = 12x - 2y + 23 that is nearest to the point…

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Q: Find the length of the curve with equation x2 (y + 1)3 from the point where æ = 0 to the point where…

A: Since the given curve is  x2=y+13      from point x=0 to x=33. Given curve can be written as x=y+132…

Q: Find the coordinate of the extrema of the curve y = x² – 4x + 1.

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Q: Determine the parameter equation of the following curve x2 + y2= 5

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Q: Given the equation of curves: y = x2 + 7x + 6 and x - 2y = 6. Find the slopes of the tangents of the…

A: We begin by finding the points(s) of intersection of the 2 curves y =x2+7x+6  &amp;  x-2y = 6y…

Q: Find the exact length of the curve. x = e - 9t, y = = 12e2, 0 sts 4

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Q: Find the exact length of the curve 36y? (x² – 4)³, 2 0.

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Q: Consider the curve x+y² +2xy=4x . (a) Find all the x-intercepts of the curve. (b) For each of the…

A: The given curve is: x3+y2+2xy=4x...(1)

Q: find equation for the lines that are tangent andnormal to the curve at the given point.xy + 2x - 5y…

A: Given : The equation is x y + 2x - 5y = 2 and point (3, 2).

Q: Find the point on the curve g(I) z +5 that is closest to the point (-57, 5).

A: Q - Point on the curve g(x) = x2 + 5 that is closet to the point (-57, 5).f - If point on curve is…

Q: Find the slope and concavity of the curves at the given points. r = eθ, θ = 0, π

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Q: Find the values of a and b for the curve x2y +ay? -b if the point (2, 2) is on its graph and the…

A: Given x2y+ay2=b

Q: Find the exact length of the curve.   y = 1+ 6x3/2 , 0 ≤ x ≤ 1

A: Find the exact length of the curve.

Q: Find the exact length of the curve. x = 6 + 3t?, y = 2 + 2t3, 0 sts 5

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Q: d the exact length of the curve. y = 1 + 8x3/2, Osxs1

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Q: Given the curve y= x^3 - 4x + 1 . At what point on the curve have the smallest slope? * O (0,1) O…

A: The given curve is: y=x3-4x+1

Q: After Identifying and sketching the curve for x2+25y2-4x+100y + 4 = 0, partimize the curve

A: Given: x2+25y2-4x+100y+4=0 To Find: i. Identify and sketch the curve.ii. Parametrize the curve.

Q: find equation for the lines that are tangent andnormal to the curve at the given point.x^3/2 +…

A: Given: x32+2y32=17    at the point (1,4)

Q: Find the equation of the new curve C obtained when the graph of the curve C with the equation x 2 −…

A: Find the equation of the new curve C obtained when the graph of the curve C with theequation x 2 −…

Q: Find the exact length of the curve. y = 2/3x3⁄2,    0 ≤ x ≤ 1

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Q: Find the points on the curve as results of the intersection of x² + y? + z? – 2z = 0, y+ z = 1, -…

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Q: Given that y" = 2x, find the value of y when x = 3 if the curve passes through the point (-1,); and…

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Q: find equations for the lines that are tangent,and the lines that are normal, to the curve at the…

A: Given: xy+2x-5y=2; 3,2 for finding equation of tangent, we need to find slopem1 of tangent  we know…

Q: Sketch the figure of the described situation in the problem and then solve. Determine the equation…

A: Tangent and normal line: At the point of tangency, the normal line is defined as the line that is…

Q: Find the exact length of the curve. y = 3 + 8x3/2, 0<x<1

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Q: find equations for the lines that are tangent,and the lines that are normal, to the curve at the…

A: Solution:- The given curve is  x+xy=6  ......(1) and point (4,1) we have to find equation of the…

Q: Q4\ Find an equation for the tangent line drawn to the circle (x- 3)2 + (y+ 3)2 = 50 at the point P…

A: Here, the given equation of the circle is (x-3)2+(y+3)2=50. We need to find the equation of the…

Q: Find the coordinates of the point in the curve y = 12x – 2y + 23 that is nearest to the point P(10,…

A: Given curve: y2=12x-2y+23 The point is  P10,4 To find: The coordinates of the point on the curve…

Q: / Find the length of the curve y = (÷) (x²

A: Given,         y=13x2+232

Q: Find the exact length of the curve. 36y? = (x2 – 4)3, 5< xs 6,

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Q: r= g° ,0<g<\5

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Q: Find the angles at which the curve y=x3−x intersects the x-axis.

A: The angle at which curve intersect the x axis is determined by the angle of slope of tangent to the…

Q: 11. Find the slopes of the curve y y?- r2 at the two points shown hcrc. 2 (V3 = y2 - x?

A: we have the curvey4=y2-x2

Q: Find the equation of the curve for which y" = x, and which passes through the point (1, 2) with a…

A: NOTE: Refresh your page if you can't see any equations. . take integration  ...............(1) at…