Determine the equation of the directrix of the curve 3x=2y2-4y+7 a. x=30/20 b. x=30/24 b. x=31/20 d. x=31/24

Q: Eliminate the parameter to find a cartesian equation of the curve. x = et,  y = e-4t

A: A curve is a two dimensional object with equation of the form y=f(x). This equation can sometimes be…

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: 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 described by the parametric equations. x = 5 + 6t², y = 3 + 4t³,…

A: Find the length of the curve   x= 5+t2 ,y= 3+4t2 , 0<=t<=1 .

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

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Q: Find the equation of y, glven the derlvative and the Indicated polnt on the curve. dy = 2x- 1 xp

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Q: Find the exact length of the curve a 1+ 3t", y = 4+2t", 0 <ts1.

A: Exact answer is 2(2√2 -1)

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

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Q: Find the exact curve x = (y4/8) + (1/4y2), 1 ≤ y ≤ 2

A: First we find the graph of the function in the given region with the help of some points:   In the…

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 dy if the curve is described by the equation x³ 4x³y + 3y² +Ske y

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Q: State the following curve in the form of a parameter equation a. y = 1-x², z = -2 b. y²-z²=9, x =4

A: a. According to question,Given equation,y = 1-x2 ,  z = -2

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

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

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

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Q: Find the exact length of the curve described by the parametric equations. x = 5 + 3t2, y = 3 + 2t,…

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Q: dy 20 yx %3D

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

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Q: (b) Eliminate the parameter to find a Cartesian equation of the curve.   for  −5 ≤ y ≤ −1

A: The parametric equation of curve are x=1-t2 y=t-3

Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x 1+lnx b) y = -

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Q: find the slope of the parametric curve x=-6t-5, y=3t^3, at the point t=3

A: To find the slope we have to find dy/dx For that we find dx/dt and dy/dt first

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 an equation of the curve that satisfies dy 33ya10 dæ and whose y-intercept is 4. y(x) =

A: Given: dydx=33yx10 and y-intercept is 4. To find an equation of the curve. Solution: Separating the…

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: y =(+ + +)* x = 4t + 1, 4

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Q: Find an equation of the curve that satisfies dy 20ya de and whose y-intercept is 3.

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Q: The family of curves orthogonal to x2 + 4y2 = c2 has the general equation 04. %3D

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Q: Graph the curve defined by the parametric equations

A: Here given parametric equation as x=3t2,  y=2t, -2≤t≤2 Then t=y2

Q: Q3/ Find the angle between two curves: 3 x2 , y = x² y = 2

A: Please see the answer in step 2

Q: (b) Find a rectangular-coordinate equation for the curve by eliminating the parameter.

A: Given equations in the parametric form as:x= cos2(t), ............................(1)y = sin2(t)…

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

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Q: Sketch the following curves. 33. y = 2x + 3x2 + 1 %3D

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Q: -Obtain the Cartesian equation of the curve by eliminating the parameter. 14) x = t - 3, y = t2 + 5…

A: To obtain the Cartesian equation of the given curve.

Q: Find the slope of the parametric curve x = -2t3 + 1, y = 3t2, for - ∞ &lt; t &lt; ∞, at the point…

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Q: Evaluate (2 - xy) ds where C is the curve given below. -2 -1 -2

A: Given   ∫C2-xyds Curve C

Q: Eliminate the parameter to find a Cartesian equation of the curve. x=2 sint, y=3cost, 0st<27

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Q: Graph the curve whose parametric representation is given. x-iy-4t + 3; 0sts4 B) D) 10- -10

A: we have to draw the graph of given parametric equation

Q: 6x 4. У3 y = х+3

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Q: Eliminate the parameter t to find a Cartesian equation of a curve. x = 1 + 3t,  y = 2-t^2

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Q: Eliminate the parameter to find a Cartesian equation of the curve for −2 ≤ y ≤ 4. x = t2 − 3,…

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Q: Eliminate the parameter to find a Cartesian equation of the curve. x = t2,    y = t5

A: A curve is a two-dimensional object with equation of the form y=f(x). Curves can be parameterized to…

Q: The curves x=y²and x = 2 y – y?

A: Since you are asking multiple questions. As per our guidelines, we are supposed to answer only one…

Q: Find the slope of the line whose parametric equations are x=4t+6 and y=t-1

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

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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 a rectangular-coordinate equation for the curve by eliminating the parameter. x = et, y = e-t

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Q: The given curve is rotated y = 3 - x2,

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Q: 4. (x – h)? + y² = c²

A: The solution are next step

Q: Given the parametric curve: x = t3-6t2 y = t2-4t What are all the points that the curve passes…

A: Given: the parametric curve: