Suppose point A(9,10) was rotated 270 degrees counterclockwise around the origin.  What is the y coordinate of A'?

Q: Give a vector parametric equation for the line through the point (3, 1) that is perpendicular to the…

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Q: 5) Find the orthogonal trajectory of the family of curve given by y = In(r+b) %3D

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Q: find a parametrization for the curve. the line segment with endpoints (-1, 3) and (3, -2)

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Q: Find parametric equations for the normal line to the surface z=-7x2 -9y2   at the point   (2,1,-37)

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Q: Find the parametric equation for a line that is tangent (intersection) of the two fields below: −2x…

A: We have to find parametric equation for a line that is tangent (intersection) of the two fields…

Q: Find the parametric equation of the line that passes through point P(2,3,4) and is perpendicular to…

A: To Determine: Find the parametric equation of the line that passes through point P(2,3,4) and is…

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: Find the vector parametric equations of the two straight lines tangent to the given space curve

A: Given,              rt=2t2+3i+15t-7j+4t2+5kand  passing through the point P-3, -22, -7.

Q: Find parametric equations of the line through (-1,0,1) that is parallel to 2i – 6 j+ k. -

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Q: (3) Find a parametric equation for the line segment joining (1, 0, 1) and (0, –2, 1).

A: The direction vector of the segment is: (0,-2,1) - (1,0,1) = (-1, -2, 0) Initial point is (1,0,1).…

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: What kind of conic section is given by the quadratic form ? -11x,2 + 84x,x2 + 24x,2 = 156 Transform…

A: Given Quadratic Equation is, -11x12+84x1x2+24x22=156 Matrix Representation form is, A=-11424224 Find…

Q: Find three different parametrizations of the graph of y = x3.

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Q: Consider AXYZ with vertices X(4, 7), Y(8, 5). and Z(6, 3). Follow the steps to the left to find the…

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Q: Find parametric equations and a parameter interval for the motion of a particle starting at the…

A: Given,

Q: Find a parametric representation of a straight line passing through (1,2,1) in the direction of…

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Q: The scalar equation of the line perpendicular to (x, y) = (5, 2) +r(1, -3) through the point (2, -2)…

A: The scalar equation of a line is of the form Ax+By+C=0

Q: Find the parametric equation for the line through the point (2,-3,1) and parallel to the vector…

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Q: Find a parametric representation of a straight line through (1,1,1) and (4,0,2), and sketch it using…

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Q: A robot begins moving on a linear path at (2, 1). When it reaches (5, 2), the robot turns 90°…

A: We have to find the y-coordinate.

Q: What is the minimum angle of rotation (in degrees) that will carry the six-sided star onto itself: I…

A: It is a 6 sided star that means it will redivided into 3 parts:⇒ we divide 360°( full rotation ) by…

Q: Obtain the dirfferential equation of the family of curves:  1. All circles passing through the…

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Q: Two children weighing 16 and 24 kilograms are sitting on opposite sides of a seesaw, both 2 meters…

A: Given,           Two children weighing 16 and 24 kilograms are sitting on opposite sides of a…

Q: What is the image of the point (4, 0) after a rotation of 90 counterclockwise about the origin

A: Under rotation 90° counter clockwise about the origina point (x,y)→(-y,x)Hence (4,0)→(0,4)

Q: Find the polar coovdinates rectanguar coordinak es the point whose (x,y)= LI,}) are

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Q: Find parametric equations of the line through (–3, 0, 3) that is parallel to 5i – 8j+ k. x(t) y(t)…

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Q: Find a parametrization for the line SEGMENT between (- 5, 7, 6) and (2, – 6, – 9). |

A: Parameterizing a line segment, which joins the points (x1,y1,z1) and (x2,y2,z2), helps in obtaining…

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: Find parametric equations for the line pass- ng through the point P(1, –1, 3) and perpen- licular to…

A: Given that: Line is passing through P(1,-1,3) and perpendicular to the plane:       4x+3y-2z=6.

Q: Find the linear speed v for a point on the edge of a flywheel of radius 2 m, rotating 42 times per…

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Q: Find parametric equations for the line segment thatgoes from Q(0, 3) to P(-2, 0).

A: Given Q(0,3) and P(-2,0)

Q: find The unit Vectors tanent and normal to The ellipse x+2y= 6 at The Point (2,1).

A: Given, ellipse x^2+2y^2=6   point=(2,1)

Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 4x+2y…

A: Let F(x,y,z) define a surface that is differentiable at a point (x0,y0,z0), then the normal line to…

Q: Find parametric equations for the lines in The line through (1, 1, 1) parallel to the z-axis

A: Given: 1,1,1 parallel to z-axis

Q: 3. Find the parametric equation of the line passing through the point (-1,0, 3) and in the direction…

A: Equation of the line passing through the point (-1,0,3) in the direction N(7,0,-2) is   ( x+1)/ 7 =…

Q: Give a vector parametric equation for the line through the point (−1,−1) that is perpendicular to…

A: Vector equation of line which passes through point r0 and perpendicular to line a+bt,c+dt is given…

Q: What kind of conic section is given by the quadratic form ? -11x,? + 84x,x2 + 24x2? = 156 Transform…

A: Given quadratic form is-11x12+84x1x2+24x22=156The above conic is determined and transformed to…

Q: Give a vector parametric equation for the line through the point (4, 0, -5) that is parallel to the…

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Q: 3. Find the parametric equation of the line passing through the point (-1,0,3) and in the direction…

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Q: Which of the following point is the projection of the point (0, 4, 2) on the yz-plane?

A: In this question we have to find the projection of the point on the yz-plane.

Q: 9. What will be the coordinates of point Nafter a 270 counterclockwise rotation about the origin?

A: When rotating a point 270° counterclockwise about the origin our point N(x,y) becomes N'(y,-x). This…

Q: Find the equation in the x'y 'system obtained by 45 rotation of the curve whose equation is xy = 1…

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Q: Find parametric equations for the line through the point (0, 1, 2) that is perpendicular to the line…

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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: 3. Parametrize the circle of radius 5 having centre (8, –3) and hence find a tangent vector and the…

A: We have to find parametric equation, tangent vector and tangent line for the given circle.

Q: Q2 What are the parametric equations for the line through the point (6,-3,1) that is orthogonal to…

A: We have to find the equation of parametric line

Q: Find the general equation of the plane through the point (3, 2, 5) that is parallel to the plane…

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Q: Which of the following is the cylindrical coordinates of (-1, -/3,2)?

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Q: Find the parametric equations of the line that is perpendicular to the plane 2x +y +3z = 4 and goes…

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Q: Find the distance between point A(3, 4, 4) and the line of parametric equations x = -1-t, y = -t, z…

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