3. Plot both the following curves on the same set of axes. r = 5 - 4 cos e and the parabola y = r.

Q: Which one of the following could be the graph of the curve given parametrically by x(t)=t^3 -2t,…

A: x(t)=t3-2t y(t)=3-t2

Q: Find the equation of tangent to the circle x + y = 25 at the point (3, –4) 25 O a. y = 7x 4 13 25 O…

A:

Q: Find the arc length of the graph of the given equation from A to y = 6x2/3 + 1 А(-1,7), В(—8,25) B.

A:

Q: Find the lengths of the following curves: b. x = cost and y = t + sin t, 0<t<n

A: we have to find the length of the given curve

Q: Find the length of the arc of the curve in the given range, y3 1 x = 16y + 4y? ++ 0sys4 4(y + 4) '

A:

Q: nd the equation of the tangent to the circle X^2+Y^2-8X+2Y+7=0 at point (3,2), given that point…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the point (a, b) on the graph of y = ex where the value ab is theleast.

A:

Q: (11) At what point do the curves ri(t) = (t, 2-t, t²) and r3(s) = (1-s, s+1, s²+1) intersect? Find…

A:

Q: For what values of a and b is the line 5x + y = b tangent to the parabola y = ax? when x = 4?

A: y=ax2y'=2axy'(4)=2a(4)y'(4)=8a Now we have 5x+y=b ⇒y=-5x+b Compare with the equation y=mx+b From…

Q: = V4 cos" : – 1, y = 10 < x < 30

A:

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

A:

Q: The parabola y = x2 + C is to be tangent to the line y = x. Find C.

A: To find the value of C.

Q: Find the points on the curve x^2y = 2 nearest the origin.

A:

Q: 13. Eliminate the parameter t, sketch the curve, and indicate the orientation. x=5 sint, y= 5cost,

A: We will square the both equations and then we will add them to eliminate the t

Q: Find the Lengeh fror the foclowing Curves Dr= I+ Cos9 D rel-coso |

A:

Q: 1 use the formula L= [, ct to find the length of the curve 1 X=-ť. y = 1 for 0St<1

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Q: Find the length of the arc of y=x^(3/2) between the points (1,1) and (4,8).

A: Find the length of the arc of y=x^(3/2) between the points (1,1) and (4,8)

Q: It is known that at a distance of 1.5 metres from the siren, the sound intensity is 4 watts per…

A:

Q: (d) Find the points on the curve x'y = 60 nearest the origin.

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Q: Find the equation of the tangent line to right branch of the hyperbola π π ㅠ x = sect, y = tant, st≤…

A:

Q: Find points P and Q on the parabola y = 1 – x² so that the triangle ABC formed by the x- axis and…

A: We have △ABC is an isosceles right angle triangle. So the interior angle at B and C must be 45° The…

Q: Find the points on the curve 5x + 5y? - 6xy - 6xy = 4 nearest to the origin.

A:

Q: Find the points on the curve y = 14x closest to the point (0, 1). and

A: This question is based on application of Derivative.

Q: Find the exact length of the portion of the curve shown in b r = 0+ 2 2 (i)

A:

Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax2 when x = 5? a = b…

A: Given: The line 4x+y=b is tangent to the parabola y=ax2 when x=5. To Find: Value of a and b.…

Q: For what values of a  and b  is the line 2x  + y = b tangent to the parabola y = ax 2   when x = 2

A: Given line is 2x+y=b Given line can be written as y=-2x+b On comparing with equation of line y=mx+c,…

Q: - Find the equation of the tangent to the circle x2 С. Зх + 5y + D. Зx - 5y + А. Зх + 5y -34%3D0 B.…

A: Find the equation of the tangent to the circle x² + y2 - 34 = 0 through (3, 5).

Q: (x – 2)2 + y² = c² %3D

A:

Q: At what point do the curves r¡(t) = (t, 1 – t, 3 + t²) and r2(s) = (3 – s, s – 2, s²) intersect?…

A: Given Data: Curve 1: r1t=t, 1-t, 3+t2 Curve 2: r2s=3-s, s-2, s2   For the intersection point,…

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 arc length of the graph of the given equation from A to B (x+3)2 = 8 (y-1)3 A(-2,3/2)…

A:

Q: 7. For whit value of b will the line y =- y 3x +4x -1? 2x+ b be tangent to the parabola

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

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Q: 6. Show that the line with equation y = 3x – 5 is a tangent to the circle with equation x² +y? + 2x…

A: Equation of line : y=3x-5 Equation of circle : x2 + y2 +2x -4y -5=0 We have to prove that the line…

Q: Graph the curve: x = 3et cos(t),    y = 3et sin(t),    0 ≤ t ≤ π and then find the exact length of…

A: The provided parametric equation of the curve is as below

Q: No calculators. Find the exact length of the curve. 0≤x≤l y=2+2x³/2,

A: Length of the curve  =∫ab 1+f'(x)2 dx .

Q: 2 Consider the two graphs y = 2x and x - xy + 2y = 28. The absolute value of the tangent of the…

A: Introduction :

Q: Find the length of the following curve (a) x = 2t , y = cos 4t, 0 <t<

A:

Q: Find the length of the arc of the curve in the given range, y3 +. 3 1 x = 16y + 4y² + 0 < y< 4…

A:

Q: 3x + xy? 2y + x?y dy dx

A:

Q: b. the length of the tangents from the point (2, 5) to the circle x +y² -14x-2y+34= 0

A:

Q: At what points do the curves y=x2 and y=√x intersect? Find the angles of intersection between the…

A:

Q: b) Find the points on the curve 2 17x + 12xy + 8y“ = 100| that are farthest away from the origin…

A: Substitute x = rcosθ and y= rsinθ

Q: At what point do the curves r₁(t) = (t, 5 − t, 35 + t²) and r₂(s) = (7 — s, s − 2, s²) intersect?…

A:

Q: Find the exact length of the curve. x = Vy (y - 3), 9 < ys 25

A: It is given that x=13yy-3, we need to find the exact length of curve.

Q: Find the exact length of the curve. y = In(sec x), 0s x s a/3

A: This question is based on application of Derivative.

Q: 4. (x – h)? + y² = c²

A: The solution are next step

Q: ind an equation of the tungent line to y= 45in2 X at point (i II

A:

Q: 2. Find the equation of the tangent to the circle x2 + y2 +4x +16y - 32 = 0 through (4, 0).

A:

Q: Question 5 Find the length of the curve. +- from y = 1 to y = 2 %3D 4y2 2

A: