5. Eliminate the parameter to find the equation of the ellips Sx(t) = 4 cos(t) + 1 ly(t) = 3 sin(t) %3D

Q: 1.1 Find all the points on the curve x²y² + xy = 2 dy if y = x sin() dx 1.2 Find

A: Note the result : The equation represent a equation of rectangular hyperbola .The points on the…

Q: 4) Find the critical points of the parametric equations x = t* - 1 y = t3 - t

A:

Q: 1. Find the equation of the tangent line (s) to the following set of parametric equations at the…

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Q: 2. Write an integral expression to represent the length of the path described by the parametric…

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Q: 5. Eliminate the parameter to find a Cartesian equation of the following curves. et (a) x = vt+1, y…

A: Eliminate parameter t.

Q: [(VxA)• dS over the surface of a hemispherical b 2 and its circular rim if A = 3 sin()â

A: Sol

Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 6, y = a sin 2 0 from e…

A:

Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 0, y = a sin 20 from 8 =…

A: We are asked to find the length of the curve whose parametric equations are as follows:…

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: 3. Deduce from the orbit equation (1 + e)ro 1 + e cos 0 that a planet is closest to its sun when 0 =…

A:

Q: Find the speed at t = π/4 of a particle whose position at time tseconds is c(t) = (sin 4t, cos 3t)

A:

Q: dy 2y ! = -x² y² sec²x %3D dx +

A: Using solution of Bernoulli Differential equation.

Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint); + In…

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Q: Compute sin z dz , where a is the piece of the parabola with equation y= a?, which lies between the…

A:

Q: 8. Given the space curve r(t) = (sin²t, cos't, tant), find an equation of the tangent line in…

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Q: Eliminate the parameter to find the cartesian equation of the curve: x = 2 sin 0, y = cos² 0, sos…

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Q: |3| 7/7 2) Find the arc length of y = ln (sec x) from x = 0 to r 11

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Q: Given parametric equations x = 2 cos 0 and y = sin 0. d²y Then dx2 in the point (V2,) is

A: Given parametric equation is  x=2cosθ and y=sinθ

Q: C) Find the equation of tangent to the curve 4x +9yi = 36 at the point (3 cos 0, 2 sin 0).

A:

Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint)j + In…

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Q: 3. Find T (t) and a set of parametric equations for the tangent line to the helix given by ř(t) = 2…

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Q: 33. (a) Show that the total arc length of the ellipse x = 2 cos t, y = sint (0 <t< 27) is given by…

A: Given: x=2cost  , y=sint   0≤t≤2π To show : The length of total arc is  4∫0π21+3sin2tdt

Q: Find the slope of the line tangent to the polar curve at the given point. 3 7n 2' 6 r= 3 sin 0; dy…

A: Compute the slope of the line tangent to the polar curve as follows.

Q: T c •sinx, S* San* (1 + cosx)dydx 0, 0.

A: Given: The integration ∫0π∫0sinx1+cosxdydx To determine: The value of given integral.

Q: 4. Find the slope of the curve r = cos 20 at the origin 5. A particle moves along a path whose…

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Q: Find an equation y = f(x) for the parametric curve c(0) = (cos(0), 10 cos(0) + 3 sin? (0) and…

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Q: Match the equation to the graph. y 2 sin 30 - 1 %3D Sn / 3n 7n 21 4.

A: y=2sin3θ-1Use the form  a sin ( b x − c ) + d  to find the variables used to find the amplitude,…

Q: 33. tan- (z²y) = x + xy°

A:

Q: 1. Find the equation of the tangent line to the curve: x = Vt, y = e² at t=1. d?y at t=1 for the…

A: Solve by using differentiation.

Q: 4) Find the critical points of the parametric equations x = t* – 1 y = t3 -t

A: Topic:- application of derivatives

Q: Q3 Find dy/dx on the graph y sec/x+ y? = cos2x at point (1, 2).

A: We have to find dy/dx at (1,2).

Q: 1. Consider a fence whose base is the path with parametric equations |x(t) = cos³ t, |y(t) = sin³t,…

A: Given, A fence whose base is the path with parametric equations xt=cos3tyt=sin3t for 0≤t≤π2. Let the…

Q: FIND Y(s) OF THE GIVEN EQUATION. y" + 4y = cos(t-3)+4t, y" - 6y + 15y = 2 sin(3t), y(3)=0_y' (3)=7 y…

A:

Q: 1. Find the arclength of y= (4 -x3,3/2 from x = 1 to x = 8.

A: The arclength of given equation

Q: (11) Find the tangent line(s) to the parametric curve given by * = t5 - 4t3 y = t2 at (0, 4)

A:

Q: Find an equation y = f(x) for the parametric curve c(0) = (cos(0), 3 cos(0) + 8 sin²(0)) and compute…

A: The objective is to find y(x) and it's it's derivative .

Q: 4. Solve for the critical points of the given parametric equation: x = t³ – 1; y = t² + t

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Q: Ev 2 x 2 [x²z dx - yx² dy + 2 dz along the curve C'shown in the figure. AZ 2

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Q: 10. Find the equations of the two tangent lines at the (-1,0) for the parametric curve x = 12- 2, y…

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Q: 3. Find the equation of the tangent line to the curve C given by the parametric equations x= e', y=…

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Q: 4) Find the critical points of the parametric equations x = 5 – In t y = t + Int

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Q: Determine the form of a particular solution yp for y"+y cosx

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Q: Q3 Find dyldx on the graph y sec /x2 + y cos2x at point (1, 2). ес

A: We have to differentiate the given function with respect to x.

Q: a) Find dy/dx and d²y/dx² at the given point without eliminating the parameter x= 0+ cos 0, y=1+ sin…

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Q: Find the solution to the Bernoulli Equation. (3siny-5x) dx + 2x² cotydy=0

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Q: 2. Given the parametric equations x= 2t+ sin 2t and y=1-cos 21, where t is a parameter, dx 2)

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Q: 4. Consider the circular helix given by 7(t) = (3 cos t, 3 sin t,4t). Give an equation for the…

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Q: Question 16 Find dy/dx at the glven point without eliminating the parameter, r=0 + cose and y=l +…

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Q: a. Find the solution set for log, 2+2.log3 x= log, (7x-3) b. Plot the polar curve r 2(1-cose) in…

A:

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.