(A) (B) (C) (D)

Q: Consider the curve defined by the equation 2x + y = 3xy for questions (4-6). %3D 2 1 -3 -2 -1 1 2 3…

A: The given curve is: 2x3+y3=3xy

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

A: We make table for y=2-t   Then we make table for y=-2t

Q: find a cartesian equation for the curve r2 = 14

A: Find a cartesian equation for the curve         r2 = 14

Q: Find the equation of the circle that passes through (1, 0) and (0, 1) and is tangent to the x-

A: Here we have to find the equation of the circle that passes through (1, 0) and (0, 1) and istangent…

Q: Sketch the given curves together in the appropriate coordinate plane and label each curve with its…

A: Sketch the given curves together in the appropriate coordinate plane and label each curve with its…

Q: Discuss the properties of the curve and sketch fully (drawn to scale) 1) Y = 3x5 - 5x3 + 4

A: Find the attachment

Q: the points where the curve meets the axes.

A: y= (x-2)(x+1)(x+2) When x=0, y=-4 When x=1, y=-6 When x=-1, y=0 When x=2, y=0 When x=-2, y=0 When…

Q: Find the exact length of the curve. x- 2, y =? - 2, Osts9

A:

Q: Consider the curve y = 3x3, The sketch of the portion of this curve between x = - 1 and x = 8 is…

A:

Q: Does the point (1, 1, 1) belong to the curve and if so, to which t does it correspond? Yes, t=-1 and…

A: The equationof the curve is r(t)=( t, t3, t6 ) , t≥0For t=1, So ( t, t3, t6 )=( 1,13 ,…

Q: Identify the curve by finding a Cartesian equation for the curve r = 4secθ

A: The given curve is,

Q: State the following curve in the form of a parameter equation a. y = 1-x², z = -2 b. y²-z²=9, x =4

A: a. According to question,Given equation,y = 1-x2 ,  z = -2

Q: Q2- Sketch the curve: y = (x+1)

A: The function given to us is  y=x(x+1)2

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

A:

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: Sketch the given curves together in the appropriate coordinate plane and label each curve with its…

A: Given, y=3-t   and  y=-3t

Q: b. The curves y = x² - 5x and y= 25-x.

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: (b) Eliminate the parameter to find a Cartesian equation of the curve.   for  −5 ≤ y ≤ −1

A: The parametric equation of curve are x=1-t2 y=t-3

Q: 1. Find the standard form of the equation of the circle tangent to both axes at (-3,0) and (0,3).

A:

Q: y =(+ + +)* x = 4t + 1, 4

A:

Q: find a Cartesian equation of the curve

A:

Q: Find the length of the curve.  y = (9 - x^2/3)^3/2 from x = 1 to x = 27

A:

Q: The graph, when the curve y = √3 + x² from x = 0 to x = 4 is rotated about x - axis is A B C D

A: To find the graph of the solid formed by rotating the given curve about x axis, first we find the…

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

A:

Q: (b) Find a rectangular-coordinate equation for the curve by eliminating the parameter.

A: Given equations in the parametric form as:x= cos2(t), ............................(1)y = sin2(t)…

Q: Let P(0) be the terminal point of 0 on the unit circle. What is its x-coordinate if y = b – 1?

A: P(θ) be the terminal point of θ on the unit circle.

Q: Eliminate the parameter to find a Cartesian equation of the curve.

A: Given  x=sin(t)  y=csc(t) and 0<t<π/2 We need to find the Cartesian equation and graph

Q: The equation of the curve is given as y = 3x + 1

A: topic - slope of curve at a point

Q: sketch the curve r=1-3costheta

A:

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: DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. Y = 3x5 – 5x3 + 4

A: Given The equation is y=3x5-5x3+4.

Q: Find the exact length of the curve. 36y2 = (x² – 4)3, 2 < x < 9,

A: Given:  36y2 = (x2 - 4)3 , 2≤x≤9,y &gt;= 0

Q: Find the coordinates of the point/s on the curve y = 2x? which are closest to the point (9,0).

A: We have to find the closet point to the point    (9, 0)

Q: At what part of the curve 2x2 + y? = 8 does it assume the highest value?

A:

Q: 4. Convert the equation r =8cos0– 2sin0 to Cartesian coordinates and fully describe the resulting…

A: see below the answer

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

A:

Q: Determine the length of the curve x = (y-1), where 4 <y <9.

A: Now differentiating given curve with respect to y, we get

Q: Find the exact length of the curve. y = = 0 < x < 6

A:

Q: Find the exact length of the curve. y = 5 + 8x/2, 0<x<1

A: Topic = application of derivatives

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

A:

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

A:

Q: 24xy = y* + 48 dr y = 2 ke y = 4 а.

A:

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…

A:

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

A:

Q: find a cartesian equation for the curve r=3cos(θ)

A: Cartesian equation for the curve is r=3 cos(θ)   Now x=r cos(θ)  …….. equation(1) cosθ=xrr=3xcosθ…

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.