Adjust the bounds of t in the parametric function so that it goes between the two blue points, (1,-1) and (4,2), but not beyond them. Right now, t goes from 0 to 1.
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- Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.Find a parametric description for the curve x=y^2-9 from (0, 3) to (-5, -2) such that t=0 corresponds to (0, 3).5. Determine the parametric equations of the line of intersection of the planes x + 2y + z = 1 and x - y + 2z = -8
- Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid 6x2 + 4y2 + 5z2 = 30 at the point (−1, 1, 2). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)find parametric equations for the line tangent to the curve of intersection of the surfaces at the given point. 1. Surfaces: x + y2 + z = 2, y = 1 Point: (1/2, 1, 1/2) 2. Surfaces: x3 + 3x2y2 + y3 + 4xy - z2 = 0, x2 + y2 + z2 = 11 (1, 1, 3) Point: 3. Surfaces: x2 + y2 = 4, x2 + y2 - z = 0 Point: (sqrt(2), sqrt(2), 4)Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid 3x2 + 2y2 + 6z2 = 29 at the point (−1, 1, 2).
- find parametric equations for the line tangent tothe curve of intersection of the surfaces at the given point. urfaces: x2 + y2 = 4, x2 + y2 - z = 0 Point: (√2, √2, 4)Find the 1st and 2nd Derivate of y with respect to x from parametric equations. x=(t-2)5/2 y=t3-5Find a parametric equation of a line that passes through the point (1,3,-4) and is perpendicular to the plane -2x+y-5z=1 a) x=-2+t, y=1+3t, z=4+5t b) x=1-2t, y=3+t, z=-4-5t c) -2(x-1)+(y-3)-5(z+4)=0 d) (x+2)+3(y-1)-4(z+5)=0
- Find the parametric equation of the line that passes through point P(2,3,4) and is perpendicular to the plane 3x + 2y- z = 6Find a set of parametric equations for the line passing through the point (2, 0, 9) that is parallel to the plane given by x + y + z = 5, and perpendicular to the line x = −1 + t, y = 1 + t, z = 10 − t.