(c) Given that y = x4 – 8x²

Q: The cartesian equation of the curve x = vt ,y= 1– t is : (a)y = 1 – x², x 2 0 (b)y = 1 – x ,x 2 0…

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Q: : Find the orthogonal trajectories of the family of curves y4 = kx³. (A) 2y³ + 3x² = C (B) 2y³ + 2x²…

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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: The cartesian equation of the curve x = VE .y 1-t is :

A: The characterstics eqaution of the curve is

Q: : Find the orthogonal trajectories of the family of curves y4 = kx³. (A) ³ + 3x² = C (B) 2y³ + 2x² =…

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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: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

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Q: The cartesian equation of the curve x = 1-t,y= t is : (a)y = 1– x², x20 (b)y =1-x ,x 2 0 (c) x = 1 –…

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Q: The cartesian equation of the curve x = vt ,y= 1-t is: (a)y = 1 – x2, x 2 0 (b)y = 1 – x ,x > 0 (c)…

A: Given:-paametric equation:x=t y=1-tsince we have to find the cartesion equation

Q: (d) The curve y = x – x² from r = 0 to r = 2

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Q: Find the orthogonal trajectories of the family of curves x² - y² = (² A x² + y²=C² B) xy=C (C) x-y=C…

A: We can solve as follows

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: Parametrization is a way to change the parameters of a expression in such a way that domain of the…

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

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Q: (6) Find the points on the curve 5x2 + 6xy + 5y² = 9 which are nearest to and farthest from the…

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Q: Find the orthogonal trajectory of the given family of curves. y=c*e^(2x)

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Q: 6 Determine the position and nature of the stationary points of the functions: (a) z= 2x²y² + 4xy² –…

A: stationary points are those points of function f(X) where its gradient is ∇f(X) = 0 if hessian…

Q: Find and determine type of stationary point for ƒ(x,y)=x' – 3x² + 2xy – y

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Q: Find the orthogonal trajectory to the family of curves: y(x²+1) = Cx

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Q: Find the stationary points of the autonomous equation x˙ = x2 − 4x4. Classify each stationary…

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Q: b. The y' of the curve y 4 Vx

A: The given function is y=4x. Obtain the first derivative as follows. y'=ddx4x=ddx4 x-12=4…

Q: The cartesian equation of the curve x= vt ,y 1-t is: (a)y = 1– x2, x2 0 (b)y = 1-x,x N0 %3D (c) x =…

A: Eliminate t then solve

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 orthogonal trajectories of the family of curves y = kx'. = C (C) 3 y³ +x? = C (D) 3 y³ + 3…

A: Given y5=kx5 To find the orthogonal trajectory

Q: Find the value of c such that line y=3/2x+6 is tangent to the curve y=cx1/2.

A: Given,  line y=3/2x+6 is tangent to the curve y=cx1/2.

Q: Q.NO.2: a) Find the equation of the orthogonal trajectories of the family of curves. x²y² = 4c²

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Q: The x- coordinate of the point on the graph of y = Vx-1 at which the tangent line is perpendicular…

A: slope of tangent of the curve y=x-1 is dydx=12x-1 slope at (x1, y1)dydx=12x1-1=m1if (x1, y1) is the…

Q: The cartesian equation of the curve x = VE ,y = 1-t is: (a)y = 1-x2, x20 (b)y = 1-x ,x20 %3D (c) x =…

A: Cartesian equation is a equation which involves x and y , just I have eliminate the t from given…

Q: Consider the curve defined by the equation x(^2)+2xy+y^(3)=4. Part a: Find the local linearization…

A: Given informationDefine curved equation

Q: The cartesian equation of the curve x= f ,y = 1-t is : (a)y = 1– x², x 20 (b)y =1-x ,x 2 0 (c) x = 1…

A: The given curve is in paramatric form as following- x=√t y=1-t Where t is a parameter. To find the…

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: : Find the orthogonal trajectories of the family of curves y4 = kx³. (A) 2y³ + 3x² = C (B) 2y³ + 2x²…

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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 t to find a Cartesian equation in the form x = f(y) for: 3t2 Sæ(t) L y(t) -…

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Q: Find the values of dz/ôx and az/ðy at the points 31. z - xy + yz + y -2 = 0, (1, 1, 1)

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Q: 1. Find the equation of the tangent lines to the ellipse x² + 4y = 8 perpendicular to the line x +…

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Q: The cartesian equation of the curve x = vE .y 1-t is: (a)y = 1- x2, x 2 0 (b)y = 1-x ,x 20 (c) x =…

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Q: Find the equation of the curve for which y" = x, and which passes through the point (1, 2) with (A…

A: Given y'' = x  and the curve passes through (1,2)  with a slope of 5/2. which means y(1) =2, y'(1)…

Q: The cartesian equation of the curve x = 1-t.y vt is: (a)y = 1-x, x2 0 (b)y = 1-x .x 20 (c) x=1-…

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Q: ) Let Z = 3x2 – y². Find all points at which |VZ| = 6

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

Q: determine the parametric coordinate of the critical point of the curve x=t^2+3t=2 and y=t^2-1.

A: Curve will have critical point if it have vertical tangent or horizontal tangent . Slope of…

Q: 4) Find the orthogonal trajectories of the family of parabolas y – 3 = c(x + 1)².

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Q: 1. (a) Find an equation of the tangent plane to the graph of x² + y² + z² = 16 at (0, 2, 2√3).

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Q: Find the orthogonal trajectory of the curve x^2 + y^2 = 2 ln cx

A: Given query is to find the orthogonal trajectory of the curve.

Q: (b) Show that the points of inflexion of the curve y = (x- a) (x – b) lie on the | line 3x +a =4b.

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Q: Find the equation of tangent line to the parabola y² = 6x – 3 which is perpendicular to the line x +…

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Q: 3. Find the equation of the plane tangent to the graph of f (x, y) = 3x + 4y – xy at the point (1,…

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Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

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Q: analyze and trace the given curve y = x / (1 - x)2

A: To solve the following problem

Q: 1 Find the stationary points and state the nature of the curve y=xe.

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Q: Consider y = x2+3 /3e4x^2. Find the value of x at which this curve has a stationary point

A: Consider the given function.