4. (x – h)? + y² = c²

Q: (c) Sketch some typical members of the family of curves y = ax? + b.

A: Given the curves y=ax2+b is parabola  For a=1, b=0 y=x2

Q: 2. 3x + 4y +c = 0

A:

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. x = et - 4t, y = 8et/2, 0≤t≤2

A:

Q: Find the exact length of the curve. 4 1 X = 1<y< 3 + 8 4y2"

A: we will find the exact length of the curve.

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

A:

Q: Find the exact length of the curve. y4 1 X = 8 1sy< 3 4y2"

A: Here the formula of length of the curve is:

Q: Sketch the following family of curves. 1. 3x + cy – 12 = 0 %3D

A:

Q: Find the exact length of the curve x = 5 + 12t? for 0 <t <1 y = 6 + 8t3

A: The objective is to find the exact length of the curve x=5+12t2, y=6+8t3 for 0≤t≤1 Now, dxdt=24t and…

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

A:

Q: Find the point in the first quadrant on the curve y = x + x - l closest to the origin.

A:

Q: Find the exact length of the curve. x = 7 + 12t, y = 5 + 8t, 0sts 4

A: Given :      x=7+12t2 ,y=5+8t3 ,  0≤t≤4

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

A: Solve the following

Q: Find the exact length of the curve given by 2t2 t3 (0 <t < 5). x = Length = ||

A: Solve for the length of curve

Q: Find the exact length of the curve. x = 8 + 9t?, y = 3 + 6t, 0 sts4

A:

Q: Find the exact length of the curve. x = 1 + 9t2, y = 8 + 6t, 0 sts 4

A: Answer is mentioned below

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

A:

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

A:

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: (x – 2)2 + y² = c² %3D

A:

Q: Find the length of the curve given by x(t) = 1 + 3t² ,y(t) = 4 + 2t³, 0 <t < 1.

A: xt=1+3t2yt=4+2t3 Differentiate the above equation w.r.t."t"…

Q: Find the exact length of the curve. x = 3t2, y = 2t3 ;0 <t<2

A: Given data:     The first parametric equation is: x=3t2. The second parametric equation is: y=2t3.…

Q: Find the exact length of the curve for the parametric equation

A: Let's say the length of the curve is L.  0 ≤ t ≤ 1 Hence, the desired length will be calculated as:

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: Y = x2 ex X- %3D

A: the given equation of the curve is: y=x2e-x we have to solve and sketch the given curve.

Q: Find the exact length of the curve. x = 4 + 6t2 y = 6 + 4t3 0 sts 4

A:

Q: Find the exact length of the curve. x = 8 + 12t2, y = 9 + 8t³, 0 st< 3

A: given parametric equation of curvex = 8+12t2 ,   y = a+8t3

Q: Explain the steps required to find the length of a curve x = g1y2 between y = c and y = d.

A: It is given that x=gx for c≤y≤d.

Q: Find the exact length of the curve. 1 + 1sys 2 8 4y2

A:

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

A:

Q: Find the length of the curve defined by from = 9 to z = 10. 2 y-4lm (()²-1) =

A: find derivative

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

A: Given   ∫C2-xyds Curve C

Q: Find the exact length of the curve. 36y =(x+4). 5 5 x s 6, y 20

A: Given: 36y2=(x2-4)3,  5≤x≤6,  y≥0 Arc length of curve y=f(x) on [a, b] can be calculated by…

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

A:

Q: Find

A:

Q: For the curve y = ax3 + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

A: We have to find the value of a and b according to the given information

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

A:

Q: Find the lengths of the curves y = x1/2 - (1/3)x3/2, 1 ≤ x ≤ 4

A:

Q: Find the exact length of the curve. X = 3 + 6t2 y = 5 + 4t3 0 <ts 3

A:

Q: Use the methods of this section to sketch the curvey =  x3  -3a2x +2a3, where is a positive…

A: The curve is  y =  x3  -3a2x +2a3, where is a positive constant.

Q: Find the exact length of the curve. X = 4 + 6t2, y = 8 + 4t3, 0sts 2

A:

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

A:

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. 1 y = 1 < x < 2 4x

A: The given curve,   y=x33+14x, 1≤x≤2

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

A: Explanation of the answer is as follows

Q: Find the exact length of the curve. Y=y4/8 + 1/4y2, 1 less than or equal to Y less than or equal 2.

A: Given: Y=y48+14y2 , 1≤y≤2 As, the length of the curve, L is given by: L=∫ab1+dydx2dx According to…

Q: For the curve y= ax + bx? + 12x - 7, what values of a and b will make the tangents to the curve at…

A: