Suppose a curve is given by the parametric equations x = f (t), y = g (t), where the range of f is [1, 4] and the range of g is [2, 3]. What can you say about the curve?

Q: Consider the parametric curve defined by x = t – 7, y = t* + 13t. What is %3D - the slope of the…

A:

Q: Suppose the curve C is given by the parametric equations x=1+ \t y=e' where t> 0. Find a equation of…

A: The equation of tangent line to the curve is given below

Q: Sketch the plane curve represented by the given parametric equations x = 4 cos t + 2, y = 4cos t -…

A: We first make a table for the function t 0 π/2 π 3π/2 2π x 6 2 -2 2 6 y 3 -1 -5 -1 3

Q: find a parametric equation for the line that is per-pendicular to the graph of the given equation at…

A: 41. Here the given as  Now we let

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A:

Q: Sketch the curve defined by the parametric equations x = t2, y = t + 1, -∞ < t < ∞.

A:

Q: 1) Find the parametric equations of the line that is tangent to circle x² + y2 = 25 %3D at point (3,…

A: Given: Equation of circle: x2+y2=25 and tangent at point 3, -4

Q: The parametric equation of the line resulted from intersection of x-y 0, and z = 2 is %3D

A: Use the given planes.

Q: A curve is defined by the parametric equations a(t) = 2 cos(5t) and y(t) = -7 sin(-10t). Find .

A:

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A: Tangent to a curve at a point is a line that just touches the curve at that point and in some sense…

Q: The graph of the curve described by the parametric equations x = 2t2 and y =t³ – 3t has a point…

A:

Q: Suppose parametric equations for the line segment between (-2, 10) and (8, 9) have the form: a + bt…

A: Note: As per our company guidelines we are supposed to answer the first question. Kindly ask the…

Q: Find the parametric equation of the line that passes through P(-2, 0, 3) and is parallel to the line…

A: Given that: Equation of line is:     x=-1+3t, y=2-2t, z=3+t  and the point is : P(-2, 0, 3)

Q: Find parametric equations for the line segment joining the points (6, 2) and (9, 10). x=t, y 2+8t,…

A:

Q: Suppose a parametric equations for the line segment between (5,2) and (7,8) have the form:  x(t)=…

A:

Q: Suppose a curve is traced by the parametric equations x= 6.08 sin(t) and y = 22 -…

A:

Q: Suppose parametric equations for the line segment between (7, 3) and (3, 0) have the form: S z(t) =…

A:

Q: Given the curve with parametric equations, find the slope and the equation of the tangent line at…

A: Here we have to find the Slope of tangent line at indicated points . We are given parametric…

Q: Find the length of the curve defined by the parametric equations 3 -t, y = 3 In((t/4)? – 1) x = 4…

A: Given:- x =(3t/4)  y = 3ln((t/4)2-1)  To find:- Length of curve from t =5 to t=6

Q: find the slope of the parametric curve x=-6t-5, y=3t^3, at the point t=3

A: To find the slope we have to find dy/dx For that we find dx/dt and dy/dt first

Q: Suppose parametric equations for the line segment between (2, a(t) 6) and (0, 0) have the form: = a…

A: Explanation of the solution is given below...

Q: Eliminate the parameter in the parametric equations x = 7+ sint, y = 2+ sint, for 0sts, and describe…

A:

Q: A particle is moving along the curve given by the parametric equations x=1+t, y=1−t. Determine the…

A:

Q: Find the equations of the lines tangent and normal to the curve given by the parametric equations…

A:

Q: Suppose parametric equations for the line segment between (0, - 6) and (9, – 8) have the form: (t) —…

A: Suppose parametric equations for the line segment between 0,-6 and 9,-8have the form xt=a+bt…

Q: Which of the following is the equation of tangent line of the curve that is g by parametric…

A: We have been given the parametric equation  x=e2t, y=2cost+6sint at a point (1, 2).

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A:

Q: Graph the parametric curve x=2t-3, y=6t-7 by

A:

Q: The derivative I of the parametric equations and y=5vt is

A:

Q: The curve defined by any parametric equations X = f(t), y = g(t) is always a function.

A:

Q: find a parametric equation for the line that is perpendicularto the graph of the given equation at…

A: We have to find parametric equation for the line that is perpendicular to the graph of the given…

Q: Suppose parametric equations for the line segment between (3, – 4) and (0, 3) have the form: S ¤(t)…

A:

Q: 9. Find the exact length of the parametric curve for the given interval. x = 4t 2 - 3, y = 3t, 0 St5…

A:

Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

A: Let's find.

Q: Suppose parametric equations for the line segment between (-2, – 6) and (5, 10) have the form: S¤(t)…

A:

Q: Suppose parametric equations for the line segment between (8, – 3) and (9, 2) have the form: S¤(t) =…

A:

Q: Select the curve generated by the parametric equations. Indicate with an arrow the direction in…

A: make a table values t x=t+sint y=cost -π x=-π +sin-π=-π +0=-π =-3.14 y=cos-π=-1 -π2…

Q: Can the parametric curve (t, sin t) be represented as a graph y = f (x)? What about (sin t, t)?

A: Parametric curve is (t, sint) i.e x = t and y = sint

Q: Suppose parametric equations for the line segment between (2,4) and (−2,2) have the form: x(t)=a+bt…

A:

Q: Suppose parametric equations for the line segment between (0,-10) and (8,-1) have the form: a + bt y…

A:

Q: Suppose parametric equations for the line segment between (4, 3) and (– 1, – 10) have the form:…

A:

Q: Make a graph of the curve defined by the parametric equations X = t -5 on the interval 0 sts 3 y=t?

A: Given x=t-5 y=t2   0≤t≤3

Q: A parametric curve has the equations x =t+sin t and y= cos t. Calculate and , both evaluated at t=…

A: Use dy/dx= (dy/dt)/(dx/dt)

Q: find parametric equations for the given curve. Segment joining (1, 1) and (2, 3)

A:

Q: Suppose parametric equations for the line segment between (6, 1) and (7, 7) have the form: Sx(t) = a…

A: We have find four unknowns so we need four independent equations.

Q: 1) Find the parametric equations of the line that is tangent to circle x² + y² = 25 at point (3, -4)

A: Given, Equation of circle: x2 +y2=25 at a point (3,-4). now, parametric equation of the line is…