x2 + (y- 1)2 = 4

Q: Find parametric equations for the line through (-2,0,4) parallel to V=2i +4j -2k .

A:

Q: Find the exact length of the curve described by the parametric equations. x = 7 + 6t2, y = 9 + 4t3,…

A: Given curve :

Q: find parametric equations for the given curve. y = 9 − 4x

A: The given equation

Q: Find parametric equations and a parameter interval for the motion of a particle in the xy-plane that…

A:

Q: For the parametric equations: x = 23e-4t and y 44e5t dx (?)

A:

Q: Find the exact length of the curve described by the parametric equations. x = 5 + 6t², y = 3 + 4t³,…

A: Find the length of the curve   x= 5+t2 ,y= 3+4t2 , 0<=t<=1 .

Q: Find the parametric equation of the line ( x-3, y+6 )•( 2,-3 ) = 0

A:

Q: If x(t)=9sint+2 and y(t)=5cost+5, eliminate the parameter to write the parametric equations as a…

A: sin2t + cos2t = 1

Q: A cheetah can run at 105 feet per second, but only for 7 seconds, at which time the animal must stop…

A:

Q: find parametric equations for the given curve. y = 8x2 − 3x

A: Given- y=8x2-3x To find- Parametric equations for the given above curve.

Q: Complete the parametric equations for the line where the planes – 3x – 9y – 12z - 11x + 2y – 10z 33…

A:

Q: For the parametric equations: 22e2t and y = 47et

A: Derivative: - The derivative formula is one every of the foremost fundamental notions in calculus,…

Q: Find two different sets of parametric equations for the rectangular equation   y = 4/(x − 1)

A:

Q: Given the parametric equations, x = 3/t and y = t - 2, eliminate the parameter. y = --2 y = +2 y =…

A:

Q: Find parametric equations of the line through (-3,0, 3) that is parallel to 5i– 7j+k.

A: Recall:  The parametric equations of the line through (x0,y0,z0) that is parallel to a i+b j+c k is…

Q: Eliminate the parameter to write the parametric equations as a Cartesian equation. If x(t) = 3t – 2,…

A:

Q: Which of the following are parametric equations for the ellipse given by 9 apply. + y² = 1? Choose…

A:

Q: Find parametric equations of the line through (-3,0,9) that is parallel to 2i-6j+k. x(t)= 11 y(t) =…

A:

Q: Find the exact length of the curve described by the parametric equations. x = 5 + 3t2, y = 3 + 2t,…

A:

Q: A particle moves on a trajectory described by the parametric equations x(t)=2t, y(t)=8t, t≥0. What…

A:

Q: Cannot solve

A:

Q: Find the rectangular equation for given parametric equations x= 3t      y=t+3

A:

Q: Determine the direction angles for the line with parametric equations x = 5 + 2t, y = 12 - 8t, and z…

A: Direction angle

Q: Find the parametric equations of the line r = ⟨1, 2, 3⟩ + t(4, 0, -6⟩.

A: Given: r→=1,2,3+t4,0,-6 for any given vector equation of line r→=a,b,c+tp,q,r, parametric equation…

Q: Graph the plane curve defined by the parametric equations: x = t2 - 1, y = 2t, -2 ≤ t ≤ 2.

A: we have to graph the plane curve defined by the parametric equations: x=t2-1y=2t-2≤t≤2

Q: Write the parametric equations x = 2t – t°, y = 4 – 2t - in the given Cartesian form.

A: We are given the equation of the function in parametric form and we need to find the cartesian form…

Q: Find parametric equations for the line through (-2, 0, 4) parallel to v = 2i + 4j - 2k

A: we know that parametric equation of line which passes through point x0,y0,z0 and parallel to vector…

Q: -4t For the parametric equations: x = 48e and y = 37e5t

A:

Q: Graph the curve defined by the parametric equations

A: Here given parametric equation as x=3t2,  y=2t, -2≤t≤2 Then t=y2

Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 1) and directrix…

A: Given that Focus of the parabola is F0, 1 and Directrix is y=-1 We have to prove that y=14x2 is the…

Q: Find parametric equations, in terms of t, of the line passing through (2, 2, 12) and parallel to the…

A: Given: The line is passing through 2,2,12. Also, it is parallel to the line: x=5-9ty=2z=4+t The…

Q: Find the parametric equation of the line that passes through the point (4, -5, 0) and is…

A: We have to find the parametric  equation of the line.

Q: The motion of a particle in space is defined by the parametric equation x(t)=-t2+3t+1,in meter and…

A: To find the position of the particle, use the formula, r→(t)=x(t),y(t), where x(t) is the…

Q: Find the exact length of the curve described by the parametric equations. • x = 7+3t², y = 1 + 2t³,…

A:

Q: Graph the plane curve defined by the parametric equations:x = t2 - 1 ,  y = 2t ,  -2 ≤ t ≤ 2.

A: The given curve is x = t2 - 1 ,    y = 2t ,    -2 ≤ t ≤ 2. Sketch the graph as shown below.

Q: Sketch the curve represented by the parametric equations x = 1 + 8t,                 y = 3 − 4t…

A: x=1+8t,  y=3-4t When t=0, x=1+80, y=3-40⇒x=1, y=3 When t=1, x=1+81, y=3-41⇒x=9, y=-1 Now the graph…

Q: Let / be the line given in parametric form by the equations x = 3 +72 y = 0+32 z = -1+ 22 What is…

A:

Q: Write the parametric equations x = 4t – t³, y=2 – 3t in the given Cartesian form.

A:

Q: Sketch the curve represented by the parametric equations x = 2t/2, y = t4+ 1 (indicate the…

A: Given parametric equation, x=2t2 and y=t4+1we have to write the corresponding rectangular equation…

Q: Find two different sets of parametric equations for the rectangular equation  y = x2

A: y=x2 Let x=3t, then y=3t2=9t2 Now let x=4t, then  y=4t2=16t2

Q: Consider the parametric equations: x = 2t2, y =43t3. Find d2ydx2at the point t=18 without…

A: Given parametric equations are x=2t2 and y=43t3. To find d2ydx2 at the point t=18 without…

Q: Verify algabraically whether the parametric equation x(t) = 10-2.5t, y(t) = 1.5t and the rectangular…

A:

Q: Find parametric equations for the path of a particle that moves along the circle x 2  + (y - 1)2…

A: A particle that moves along the circle .

Q: Determine the parametric equations of the path of a particle that travels the circle:

A: Given,        (x-4)2+(y-3)2=49 Time interval is 0≤t≤2π

Q: Find parametric equations for the given curve. 9x2 + 4y2 = 36

A: Given -            Parametric equation -              We define x and y both in terms of a third…

Q: Eliminate the parameter to find a Cartesian equation of the curve with parametric equations x = et –…

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.