6. Find out what kind of conic section the following quadratic form represents and transform it to principal axes. Express T = [x, x2] in terms of the new coordinate vector y" = [y1 y2]. x,? – 12x1 x2 + x2² = 70

Q: r(t) = ti + (2tt2) intersect the paraboloid (2) At what points does the curve r(t) z = x² + y²?

A: We are asked to find the intersection point.

Q: 42. Whatever the value of p > 0 in the equation y = x²/(4p), the y-coordinate of the centroid of the…

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Q: 2 7 Find the projection of v = -1 onto the line tlof R'Igiven by the parametric equation e = tul…

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Q: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

A: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

Q: For the hyperbolic PDE u, +bu, =0 a) Find the finite difference equation, using forward for u, and…

A: Given: The given hyperbolic PDE  ux + buy = 0 a) To find the finite difference equation, by using…

Q: Find the scalar equation for the plane passing through the point P=(-5, -2, –4) and containing the…

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Q: has its vertex at the origin and has directrix at z = 38

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Q: In the Euclidean plane with fixed cartesian system Oxy, let C be the conic defined by the equation…

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Q: d) If S is projected onto the x - y plane, what is the shape of the resulting projection?

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Q: The parametric form of 3x - 2y + 10 = 0 is: O x = 2t y = 5 + 3t O x = t y = 5 + t O x = 3t y = 5 +…

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Q: 4. Find a parametric form of the curve given by 2r + 3y? - 6r + 6y + = 0 in the ry-plane with a…

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Q: Find the scalar equation for the plane passing through the point P-(5, 3,-5) and containing the line…

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Q: 8. Find a parametric representation of the line through the point P(1,0,4) and perpendicular to the…

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Q: 6. Find the projection of v = | -7 onto the -2 line l of R given by the parametric equation l = tủ,…

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Q: Below the paraboloid z = 18 – 2x² – 2y² and above the xy-plane -

A: The region D lies below the paraboloids z=18-2x2-2y2 and above the xy-plane.

Q: Find an equation of the plane tangent to the following surface at the given point. z= 6- 3x - 2y;…

A: The equation of tangent plane to the surface z=fx,y at the point a,b,fb can be calculated using the…

Q: d) A scalar equation of a line that goes through T(2, -5) and is perpendicular to the line 3x - 6y =…

A: The given line is: 3x-6y=5⇒6y=3x-5⇒y=3x-56⇒y=12x-56 which has a slope m=12.

Q: A. Find an equation of the hyperplane H in R° that passes through P(1; 3; 5; -1,4) and is nomal to…

A: Let's see the concept. Concept:- Equation of hyperplane H in R5 that passes through(p, q, r, s, t)…

Q: Find . F dR such that F(x, y) = (2y, xy – 2x) And I is the curve in the 3rd quadrant from the point…

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Q: 1. Show that the curve a(t) = (t,t² + 1, t – 1) is regular.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the scalar equation for the plane passing through the point P=(−4, 2, 10) and containing the…

A: Explained below

Q: 8. Calculate fo F • dr, where F(x, y) = y² i + (6x + 6y)j, and C is the portion of the parabola 2y²…

A: Given curve is 2y2-x=1 and points are (1,-1) to (7,2)

Q: Find the equation of the tangent to the hyperbola x² – 3y² = 1 at the point S(2,-1). A) 2x + 3y – 1…

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Q: 3. Write the scalar equation for a plane passing through (5,8,-1) and perpendicular to the line x =…

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Q: (b) Find the equation of the tangent plane to the hyperboloid r2 + 3y? – 322 = 1 at the point (1,…

A: We have to find the equation of the tangent plane to the hyperboloid x² + 3y² − 3z² = 1 at the point…

Q: (2) Find the Ualue of the constant m while the Curl of Foaoy,z) = (mxy- 2) Ĉ +cm-2)x)+(1-m)x2° Â is…

A: Please see the answer in step 2

Q: Which of the following is the orthogonal trajectories of the family of ellipses 2x² + y² = a? xy = C…

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Q: Use e- 45° to write 2x + 2.xy + Sy² + óx- 4y = 40 in the x'y'-plane. Then identify %3D the conic.…

A: The following question has been completely solved and explained below

Q: Give a parametric representation for the cylinder x^2+z^2=121

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Q: Calculate [ 12/20 ds where C is the parabola r(t) = (t, t², 0). Let 1 ≤ t ≤ 4. X

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Q: Calculate | F.dr, where F(x, y) = (x²–3y)i+(ye")j and the curve and curve C is the parabola æ = y² +…

A: We have to calculate ∫CF.dr, where Fx,y=x2-3yi+yeyj and the curve C is the parabola x=y2+1 from A1,0…

Q: 19. Which plane of the followings passes through the origin? x-4y+5z+1/2 =0 2x+3y+7z=0 4x+2y+6z=1 O…

A: If plane passing through origin  then constant value in the equation of the plane is zero.

Q: Which of the followings is TRUE for f(x, y) = x² + y² on the hyperbola zy 1.

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Q: Consider the conic below x² + 4xy+4y² – 2/5x + /5y = 0 and determine what is asked. 1) Conic…

A: As per our guidelines we are allowed to answer only three subparts of a given question.Kindly repost…

Q: Find the equation of the plane that passes through the point (2, 1,2) and is tangent to the surface…

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Q: Is it true or false that the coefficients of first order terms of the conic Ax? + Bry+ Cy² + Dx +…

A: Consider the provided question, To write the general second degree polynomial equation Ax2 + Bxy +…

Q: Use, 0 = 60°, to write the rotated conic section given below, in the x'y'-plane. x² - y² = 9 Select…

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Q: Compute the parametric equations of the line in R3 determined by the intersection of the two planes:…

A: To obtain the parametric equations of the intersection line, use the following formulae. Let n1→…

Q: Use a graphing utility to graph the conic. 7x2 − 2√3xy + 5y2 = 18 Determine the angle 0° ≤ θ ≤ 90°…

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Q: Find a parametric representation = z(t) for the upper half of = Z Iz – 4+ 2i| = 3.

A: Given to represent parametrically z=zt for the upper half of  z-4+2i=3 Let z=x+iy Then the equation…

Q: Consider the conic below x² + 4xy+ 4y² – 2/5x + /5y = 0 and determine what is asked. Translation…

A: Here, the given equation is x2+4xy+4y2-25x+5y=0. Firstly, let's evaluate the angle of rotation, θ.…

Q: Use e- 45° to write 2x? + 2xy + Sy² + 6x- 4y = 40 in the x'y'-plane. Then identify the conic.…

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Q: Let Q = 4x2 + 6xy+ 4y? . The points on the curve Q = 7 which are closest to the origin are: %3D %3D…

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Q: Consider the conic below a2 + 4xy+4y² – 2/5x + V5y = 0 and determine what is asked. 1)…

A: If we have a rotated conic with the general equation: Ax2 + Bxy + Cx2 + Dx + Ey + F = 0, then, we…

Q: What are the perpendicular generators on (D) 등 =D3 %3D (P) -= of the surface

A: Given equations are  x216-y24=z ......(1)x3=y2=z-4  ......(2) Equation of generators of the…

Q: Find the diffrential equation of for each of the curves determined by the condition that at each…

A: length of subtangent =ydydx

Q: At which points does the curve r(t)=ti+(2t -t² )k intersect the paraboloid z = x² +y? ?

A: Given: r→t=ti^+2t-t2k^ and z=x2+y2

Q: 2 Let w = z². Find the image of the first quadrant in z-plane

A:

Q: 16. Evaluate (x + V9) ds where C consists of two segments: the part of the parabola y = x² from…

A: In the given question we have to evaluate the integral ∫C(x+y)ds where C is the regionconsist of two…