Identify and sketch the curve: x2 + 25y2 − 4x + 100y + 8 = 0

Q: 4- Sketch the curve 9x - 4y = 36.

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Q: y (x+1)²

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Q: Determine the angle between the curves 2x=y2 and x2+y2-5x=0

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Q: Sketch the ff curves: a) Y = x² e* b) Y = 1+lnx c) Y = ²-4)² x-4

A: To draw the graph of asked curves you can simply make a table and find some points through the curve…

Q: Find the exact length of the curve. x = 6 + 3t, y = 9 + 2r, 0sts 5

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Q: For the curve y = 3x³ + 9x² – 27x + Locate the possible point of inflection.

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Q: Sketch the curve (2² + y*)³ = 4.x²y? 2.2

A: To sketch the graph of:(x2+y2)3=4x2y2

Q: Find the exact length of the curve. x = 9 + 6t2, y = 4 + 4t3,

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Q: Find the exact length of the curve. y = 4 + 6x3/2, Osxs1

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Q: Determine the nature of the turning points for the curve y = x^5 − 5x^4 + 5x^3 − 1.

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Q: 3. Sketch the curve: y = (x²–1)(x+2) x-3

A: y=(x2-1)(x+2)(x-3)y=(x-1)(x+1)(x+2)(x-3)X-intercept:(-2, 0), (-1, 0), (1, 0)Y-intercept:(0, 23)…

Q: Find the exact length of the curve. y 1x²-1-In(x), = 4 2 1 ≤ x ≤ 8

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Q: Find the exact length of the curve. x = 1 + 9t?, y = 8 + 6t, 0st< 3

A: Solve the following

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: Find the exact length of the curve. y = 4 + 4x3/2, osxS1

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Q: Find the exact length of the curve. x = 4 + 9t2, y = 3 + 6t, 0stsi

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Q: Find the exact length of the curve. y = 4 + 8x3/2, Osxs1

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Q: FIND THE PROPERTIES OF THE CURVE AND SKETCH FULLY   Y2 = x2+5x−4/x−5

A: Given,           y2=x2+5x-4x-5

Q: Find the curves 6x²-5x+2y=0 and 4x²+8y²=3 touch each other (1/2,1/2)

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Q: Consider the curve given by the equation 0 = y3 +xy +2ax + 1+x4  y'(0) = ?

A: Answer and explanation is given below

Q: Find the length of the curve. x = 4t, y =- 3/2,0st s9 0 st 122 3

A: Arc length of the given curve

Q: sketch the curve  y=x/(x+1)²

A: Given equation is: y=xx+12 We have to find the graph of y. The set of x and y-values are given as…

Q: Q2- Sketch the curve: y = (x+1)

A: The function given to us is  y=x(x+1)2

Q: x3 Y2 = x2-4x+4

A: To determine the properties of curve, we will need to have function, its first order derivative and…

Q: Find the length of the curve x = 1+ 312, y = 4 + 213, 0 <t < 1. Length =

A: Given,

Q: Find the length of the curve: x3 1 y = - 3 4x' 1<x< 3

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Q: dy 20 yx %3D

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Q: Find the exact length of the curve. x = 6 + 12t2, y = 8 + 8t, 0sts1

A: If x=f(t), y=f(t) on [a,b] then length of curve is L=∫abdxdt2+dydt2dt

Q: b. The curves y = x² - 5x and y= 25-x.

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Q: FIND THE PROPERTIES OF THE CURVE AND SKETCH FULLY Y^2 =x^2+5x−4/x−5

A: We are given the curve: y2=x2+5x-4x-5 Sketching the curve , we have :

Q: find the eauatjo aof the nor ma l to the curve 2. (x + 3)?y =3y-3x2

A: For any curve y=f(x), slope of tangents and normal at any point x1, y1 can be given by mT=dydx(x1,…

Q: Find the length of the curve. x- 4t°, y= 6t, 0sts 3

A:

Q: Find the exact length of the curve. x = 2 + 3t2, y = 5 + 2t3, 0sts 2

A: Given,

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

A:

Q: Find the exact length of the curve. x = 1 + 3t2, y = 9 + 2t, 0sts 4

A:

Q: Find the exact length of the curve. y = 4 + 4x3/2, oSxS1

A:

Q: Find the length of the curve: - for 1< y<3. 3 4y 4. x=

A: As we know that the length of a curve x=f(y) is given by:- L=∫ab(f'(y))2+1dy

Q: Find the exact length of the curve. x3 y = 1 + 4x 1< x < 3 3.

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Q: Find the exact length of the curve. x = 1 + 12t², y = 1 + 8t³, 0≤t≤4

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Q: 4- Sketch the curve 9x + 16y = 144.

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Q: Find the exact length of the curve. x = 4 + 6t?, y = 1 + 4t³, 0sts4

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Q: What are the coordinates of the center of the curve x2 + y2 – 2x – 4y – 31 = 0?

A: Given, To find coordinates of center for the curve x2 + y2 – 2x – 4y – 31 = 0?

Q: FIND THE PROPERTIES OF THE CURVE AND SKETCH FULLY 6. y2 = x²+5x-4 x-5

A: Given, the function y2=x2+5x-4x-5. We have to sketch the given curve. Also, find the properties.

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

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Q: Find the exact length of the curve. y = 1. 1sxs 2 + - 3 4x

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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: 4. (x – h)? + y² = c²

A: The solution are next step

Q: Find the exact length of the curve. x = 1 + 12t2, y = 4 + 8t3, 0 sts 3

A:

Q: Find the exact length of the curve. x = 1 + 9t, y = 8 + 6t, 0sts 3

A: Explanation of the answer is as follows