Eliminate the parameter t to find a Cartesian equation for: x = t^2 and y = 3 + 1t and express the equation in the form x = A(y^2) + B(y) + C

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

A:

Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: Given:    z = x2 + y2  Point: ( 5, 0, 0 )

Q: Sketch the surface..........CYLINDERS.............x2 + 4z2 = 16

A: Here we have to draw the surface of cylinder having equation  x2+4z2=16

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

A:

Q: 25 at the point ( 1, -1, 2 ).

A: Given that : The surface  8x2+y2+4z2 = 25 , point = ( 1, -1, 2 ).

Q: Determine the orthogonal trajectories of the hyperbola 3xy= 5 at the point (2, 5/6). Sketch the…

A:

Q: Find an equation of the tangent plane to the surface at the given point. x² + y² – 9z2 = 4, (-2, -3,…

A:

Q: find a parametrization of the curve. The line passing through (1, 0, 4) and (4, 1, 2)

A: Given: A line is passing through the points 1, 0, 4 and 4, 1, 2.

Q: An angle with its vertex at the origin of an xy-coordinate plane and with initial side on the…

A: We know, An angle with its vertex at the origin of an x-y-coordinate plane and with initial side on…

Q: 4.) Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

A:

Q: Find the distance from the point (3, -4, 2) to thea. xy-plane b. yz-plane c. xz-plane

A: The 3D view of the point is as below

Q: Determine the x - y coordinates 5 sin²t of the points where the parametric equation y=2 cost 0≤t≤ 2π…

A: The curve has horizontal tangent where the slope is 0

Q: Solve 3x – 6 ≥ 0 graphically intwo dimensional plane.

A:

Q: find the distance from the point to the plane. (0, -1, 0), 2x + y + 2z = 4

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: 4. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2, 5/6). Sketch the…

A: To find the trajectories of the hyperbola write dydx by dxdy  and solve the system.

Q: Find parametric equations for the normal line to the surfacez=ln(3x2 +7y2 +1)  at the point…

A:

Q: 4 Find a parametrization for the line segment with endpoints (-1,3) and (3,-2).

A: 4) To find the parametric equation of line segment with endpoints (-1,3) & (3,-2)

Q: Solve using method of variation of parameter: 4y" - y = xex/2, y(0) = 1, y'(0) = 0.

A: Let us consider a second order differential equation with constant coefficient , y''+ay'+by=Q(x) To…

Q: Find parametric equations for the line tangent to the curves of intersection of the surfaces xyz =1…

A:

Q: Find equations of both the tangent lines to the ellipse x2 +4y2 =36that pass through the point (12,…

A:

Q: Find the equation of the tangent line to the parametric curve x = 2t2 and y = 7t2 – 2t3 – 1 at the…

A: find the slope of function using the chain rule and then use the equation  of a tangent line to…

Q: Differentiate, and make sure to show all your work: y = exin(2z) %3D

A: The given question is taken from the derivative of the function in which we have to find the…

Q: 4. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch the…

A:

Q: Find the equation of the tangent line to the ellipse 25x2+ y2 = 109 at the point (2, 3

A:

Q: A particle is moving along a line in such a way that v centimeters per second is the velocity of the…

A: A particle is moving along a line in such a way that v centimeters per second is the velocity of the…

Q: Determine the center and the radius: X2 + Y2 + 2X +10Y + 1 = 0 O (-1,-5) Radius 5 O (1,5) Radius 5 O…

A: Topic-circle

Q: Find the distance between the point (0,0, 8) and the plane given by 2x – y + 2z – 1 = 0.

A:

Q: Find parametric equations and a parameter interval for the motionof a particle that starts at (a, 0)…

A: The given equation of circle at (a,0) is The general parametric equation of circle is where x,y…

Q: Find the unit vectors that are parallel to the tangent line to the parabola y = x² at the point (5,…

A: Given: y=x2 at the point (5,25)

Q: The equation of a curve is y = 4x³ + px², where p is a positive constant. Find the stationary points…

A:

Q: What is the equation of family of central conics with common foci and axis. Determine its orthogonal…

A:

Q: Convert x = = ln(2t) and y = 1² from parametric to rectangular form. 2

A: Given,  x=ln(2t) and y=12t2

Q: parametrik equaton of Hhe Jine thfeugh and Find Use Y For the parameter

A: Parametric equation of a line passing through a point P and parallel to a vector v is  u→(r)=P+r.v→…

Q: 2-g(%,y)%3D플-플 * at (VT ,1)

A:

Q: Haw J Express the fallasing function by Cartesian equationst 3K34tane Seco

A:

Q: parametrically

A:

Q: Find the distance between the pointx1 =−1, y1 =1, z1 =3 and the point x2 =1, y2 =1, z2 =1.

A: The first point is (-1,1,3) and the second point is (1,1,1) We will use the distance formula:

Q: Find the orthogonal trajectories of the family of parabola described by the equation (y – 3) = = cx…

A:

Q: Find an equation of the tangent plane to the surface at the given point. x² + y²5z² = 29, (-3, -5,…

A: Solution of given question is written in below steps.

Q: u =1-1,y=6-2+름 x = 1-, y = 6-

A: We have given parametric equations x=1-1t, y=6-7t+2t2. First, evaluate the first derivative dydx. To…

Q: 4. Center at (-4,9), tangent to the x-axis 5. Center at (-4,9), tangent to the y-axis

A: In this question we have to find the equation of the circle tangent to the x-axis and y-axis.

Q: At an air show, a jet has a trajectory following the curve y=2x^2. When the jet is at the point…

A:

Q: The 50 g bullet travelling at 100 ms-1 strikes the 2 kg block centrally and is embedded within it.…

A: Please check step 2 for the solution.

Q: 4. Classify the type of the equation as elliptic, parabolic or hyperbolic. Uxx xuy+xu 0 =

A: The given problem is to classify the given partial differential equation as elliptic, parabolic or…

Q: Find the distance from the point (3, -4, 2) to the xy-plane

A: Given: 3,-4,2

Q: y 1-

A: The solution is given below in the next step:

Q: Find the orthogonal trajectories of the family of parabola described by the equation (x+2} = cy.…

A: Explanation of the answer is as follows

Q: What coordinate system is suggested if the integrand of a tripleintegral involves x2 + y2?

A: Given: The integrand of a triple integral involves x2 + y2

Q: A suspension bridge with weight uniformily distributed along its length has twin towers that extend…

A: