(b) Determine the position and character of the double points on the curve x³ + x² +y² – x – 4y +3 = 0

Q: Consider 2 2.4 3 f(x) 0.8 5.5 Find the curve fitting y(x)- Ax + B

A: Let's Solve,

Q: Find the exact length of the curve. y4 1 X = 8 1sy< 3 4y2"

A: Here the formula of length of the curve is:

Q: Find the equation in the xy-plane whose graph includes x In(6t) and y = t².

A: Given  x= ln(6t) y=t2

Q: What is the length of the latus rectum of the curve x2=-12

A: Answer

Q: Let C be the curve y = 8/a for 2.1 < x < 3.8.

A:

Q: Find the x- coordinate of the inflection point(s) of the | .2* curve y = -7xr'+ 4x +10.

A:

Q: 3. Sketch the curve: y = (x²–1)(x+2) x-3

A: y=(x2-1)(x+2)(x-3)y=(x-1)(x+1)(x+2)(x-3)X-intercept:(-2, 0), (-1, 0), (1, 0)Y-intercept:(0, 23)…

Q: 1. Consider the curve C given by y = 5 + 2x3/2, 0 < x <1. (a) Find the length of the curve C.

A:

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

A:

Q: Find the exact curve x = (y4/8) + (1/4y2), 1 ≤ y ≤ 2

A: First we find the graph of the function in the given region with the help of some points:   In the…

Q: Q1. Find the length of the of the curve y -x2 X2 from x = 0 to x = 3.

A: Given curve is, y=13x32-x12 To find the length of the curve from x = 0 to x = 3

Q: The graph, when the curve y=v(3+ x^2 ) from x = 0 to x = 4 is rotated about x - axis is ....

A: This question can be solved using the concept of volume of solid generated when curve is rotated…

Q: 1 - Sketch the curve : y=-(x3– 6x²+9x+6). 6 y=Lcx³-

A:

Q: by eliminating the arbitrary constants "A" and "B" from the family of curves Ae³x y = + Be-7x O None…

A:

Q: 9. Find the point of intersection of the two curves, * y = 2r-1 y = x-2r O(-) none of these

A: To find out the point of intersection of curves.

Q: 1. Consider the implicitly defined curve Py- 2r = 25. (a) Verify that the point (1,3) is on the…

A: Given,          x2y3-2x4=25

Q: Prove that the curves x2−y2=3 and xy=2 intersect at the right angle.

A:

Q: The x coordinates of the points of intersection between the two curves y = I* and y =-I + 12z are

A: Given : y = x2y = -x2 + 12x

Q: Find the length of the curve 3y = 2(x² + 1)2 from x = 0 to x = 3.

A:

Q: (x – 2)2 + y² = c² %3D

A:

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

A: Eliminate t in given equation.

Q: Which of the following defines an equation of a plane curve that does NOT have a vertical asymptote?…

A: Given:  We have to find the equation of plane curve which has no vertical asymptote.

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: (b) the curve x = = y²-y-6 and the line x = = 2y + 4;

A: Given; x=y^2-y-6, x=2y+4

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

A:

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: Prove that the curves y2 = 4x and x2+ y2-6x+1 = 0 touch each other at the point (1,2)

A:

Q: Find the length of the curve x = y2 — 2y, 0 ≤ y ≤ 2.

A:

Q: Find the exact length of the curve. x= (y4/8)+(1/4y2), 1&lt; y &lt; 2

A: The given function is,

Q: 8. Find the equation of the surface of revolution if the generating curve, 2x – 4y = 6 is revolved…

A:

Q: Find the points on the curve x2 + xy + y2 = 1 in the xy-plane that are nearest to and farthest from…

A:

Q: Consider the implicitly defined curve xy? +3x2 = 4. %3D Verify that the point (1, 1) is on the…

A: Consider the following curve: xy2+3x2=4 Substitute x=1 and y=1 in the above curve:…

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

A:

Q: Show that the curves 2x2 + 3y2 = 5 and y2 = x3 are orthogonal.

A: To show that the two curves are orthogonal.

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-…

A:

Q: What are the coordinates of the center of the curve x2 + y2 – 2x – 4y – 31 = 0?

A: Given, To find coordinates of center for the curve x2 + y2 – 2x – 4y – 31 = 0?

Q: The point on the curve x? + 2y = 0 that is nearest to the point (0,-;) occurs where y'is A) 0 B)…

A:

Q: 1. Find the Cartesian equation of the curve represented by x = 4t + 3 and y 16t - 9, -0 <t<o.

A: Try to eliminate 't' to establish relation between x and y.

Q: Compute the length of the curve: f (x) = x² 2x, 0<x<2

A: Given:- f(x) =x2 -2x  To find:-  Length of curve over interval [0, 2]

Q: A curve C has equation y =x2lnx- 2x +5, x > 0. %3D For which values of x, the curve C is convex?

A: The equation of the given curve is  y=13x2 ln x-2x+5 , x&gt;0 For the curve to be convex its second…

Q: How far from the x-axis is the center of the curve 2x2 – 2y2 + 10x – 6y – 55 = 0?

A: The given equation of the curve is: 2x2 – 2y2 + 10x – 6y – 55 = 0 This can be written as:

Q: 27. The equation of the common tangent to the circles x+ y - 12x- 2y-123D0 and x*+y - 4x + 4y + 4 0…

A: Note: "Since you have asked multiple questions, we will solve the first question asked by you. If…

Q: The curve x = t - 3t, y = Vt intersects the y-axis when x = 0, which occurs when t = 0 and t = y 3-…

A:

Q: The x coordinate of the point of intersection between the two curves 12x y = = el2# and y = 1 is x =

A: Our Aim is to find the x coordinate of the points of intersectionbetween the two curves y=e12x and…

Q: The curve y = -x² + x + 1 opens: A. Upward %3D B. To the left C. To the right D. Downward

A: Given that the curve is         y = -x2 +x +1 Here we have to show that the curve opens in which…

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

A:

Q: Find the points on the curve x2y = 2 nearest the origin.

A: The curve is x2y=2 Let x1,y1 and x2,y2 be two points, distance betwwen these points is x2-x12+y2-y12

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.