A cubic curve has zeros 4, -5, and 6. Determine the orthogonal trajectory of this cubic curve at a y-intercept of 120

Q: 3.Write canonical forma of the second order curve and plot schematically graph: 9x2 - 25y2 + 18x +…

A: For the solution follow the next step.

Q: Determine the latera recta length of the curve 9x² + 25y² - 225 = 0

A: Solved below

Q: The curve r(t) (2t, 3 - 1,0) is a line that passes through the origin.

A: We are given a curve r(t) = < 2t, 3-t ,0 > which is a line. To find : If the line passes…

Q: suppose that an airplane main- tains a heading toward an airport at the origin. If vo = 500 mi/h and…

A: It is given that, an airplane maintains a heading toward an airport at origin, And, v0=500mi/h, w=50…

Q: Find the orthogonal trajectory of the given family of curves. y=(ce^(x))/x

A: According to the given information it is required to find the orthogonal trajectory of the given…

Q: Find the exact length of the curve. 0 < x < 6 %3D 3

A: Given:   To determine: Exact length  of the curve     Concept: Exact length of the curve y = f(x)…

Q: Find the exact length of the curve. y = 3 + 6x³/2, 0≤x≤1

A: Given :y=3+6x3/20≤x≤1

Q: Find the exact length of the curve.

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Q: Find the orthogonal trajectory of the given family of curves. (x^2)+4xy+(y^2)=c

A: Given family of curve                                               x2+4xy+y2=c we have to find…

Q: Find the curve in the xy-plane that has a slope at each point given by 1 and passes through the…

A: See attached file for a step by step explanation.

Q: Find equations of both the tangent lines to the ellipse  x2 + 4y2 =36 that pass through the point…

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Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Find the equation for the set of points in an xy-plane that are equidistant from the point P -6,3…

Q: Find the exact length of the curve. y = 5 + 8x3/2, osxs1

A: Given: y=5+8x32,   0≤x≤1

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 exact length of the curve. =글Vy (y-3), 16 <y< 25 X =

A:

Q: Find the exact length of the curve. y = 5 + 2x³/2, 0< x < 1

A: Given: y=fx=5+2x32, 0≤x≤1 we know that lengthL of curve in interval a,b is given by L=∫ab1+f'x2dx…

Q: Sketch the graph of the curve r = 2+4Cose

A: Given equation: r=2+4 cos θAmplitude: 4This equation will have the same time periodas sinθ which is…

Q: The graph of the curve described by the paramnetric equations x = 3t – 4, y = 6t + 2 is a straight…

A: Consider the curve  x=3t-4,y=6t+2

Q: Find the exact length of the curve. Vy (y - 3), 16 < y < 25 X =

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Q: Find the orthogonal trajectory of the family of curves x² + y² Cx

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Q: Determine shortest distance of the line 2x-3y-8 to the vertex of the curve x2 - 4a 4y +4 0. O 2 O…

A: We have given a line ,and find the shortest distance from vertex of parabola to line.

Q: 3. Find the line normal to the ellipse at X=-1 y= 2+4x-x3

A: Given, y=2+4x-x3 At x= -1 y=2+4-1--13y=2-4+1y=-1 Now point -1,-1

Q: 2 =(x² - 1)³/²,1 ≤ x ≤ 3

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Q: 3. Determine the orthogonal trajectory of the family of parabolas x² – y + 32x = ketch some of the…

A: The given parabola is x2-y+32x=0 ........................ (1)  Differentiate with respect to x,

Q: Show the symmetry tests for the curve r=3-3costheta

A: Consider the curve

Q: Eliminate the parameter to obtain an equation in x and y: x=-2cos2t, y=-2sin2t

A: x=-2cos2t y=-2sin2t using trigonometric property,               sin2t+cos2t=1

Q: Prove that the curves y2 = 4x and y2-6x+1 = 0 touch each other at the point (1,2)

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Q: Find the 0lar eauatiDo for the curve represented by the given Cartesian euation.

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Q: Find the lines tangent to the ellipse x2/4 + y2/9=1 that contain the point (4, 0).

A: We at first consider the equation of tangent  to x2/4 + y2 /9=1 with slope m. Then we find the value…

Q: find a cartesian equation for the curve r2cos(2θ)=1

A: r2cos2θ=1

Q: Find the point on the line y = 3x + 2 that is closest to the origin. (х, у) %3D

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Q: Draw a diagram showing two perpendicular lines that intersecton the -axis and are both tangent to…

A: The given parabola equation , y=x2. To draw two perpendicular lines that intersect on the axis and…

Q: (b) Show that the origin is a node, cusp or an isolated point on the curve y? = ax? + bx3 according…

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

A: Given curve is

Q: Sketch the curve with equation x2/3 + y2/3 = 4 and use symmetry to find its length.

A: Arc Length formula in the interval [a,b] is given by, L=∫ab1+dydx2 dx This is applied only when dydx…

Q: Show that the curve In (2X-1) , n> i has no stationary point

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Q: Sketch the curve with equation  x2/3 + y2/3 = 1  and use symmetry to find its length.

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Q: Find an equation of the normal line to the parabola y = x2 - 8x + 9 that is parallel to the line x -…

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Q: Find the points on the curve y-9x closest to the point (0, 4). ) and (O

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Q: The graph of x + z² = 1 is an ordinary right circular cylinder. Indicate axis of the cylinder lies…

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Q: Find the exact length of the loop of the curve = 3t – t°, y = 3t2 -

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

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Q: Find the exac length of the curve 3/2 , 0dxE y=2+2x

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Q: Find the exact length of the curve. 23/2 12, 0 <x < 1 y =

A: Given : y=23x32,       0⩽x⩽1   To find : Curve length

Q: 6. Show that if m is any real number, then there are exactly two lines of slope m that are tangent…

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Q: A curve on the ry-plane passes through the point (0, a) for some number a, and has the property that…

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Q: 5. The coordinates of the vertex of the curve y = 1- 2x - 4x² are: A. G ) B. (- 5 ) €(- ) D.(- -) 1…

A: Hi, for question 6 repost

Q: State the curve domain and coordinates of the point where the curve cross es the n-axis y: In (2x…

A: Given y= ln(2x - 5)  The domain of a function is the complete set of possible values of the…

Q: sketch the given curves together in the appropriatecoordinate plane, and label each curve with its…

A: Giveny=3-t , y=-3t