The Plane y=2 intersects The elliPlic Peraboloid Z=4X+ý inePerebole Find TheSLoPe oF the Tengen To The Perebole aT (0.2.16)

Q: Question Find the point (u, v) in the first quadrant on the ellipse 4x2 + y² = 4 so that the area of…

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Q: 5) x² = 12(y – 3) h =_k = _ p=- %3D %3D %3D V: focal width: F: Directrix: 10- 8 -2 -10-8-6 -4-2 2.…

A: Given query is to find vertex and focal width , directrix of parabola.

Q: Determine the type of shape the following set of parametric equations graph. v(x=t+1 ly=t2+2 A.…

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Q: *Veridy sTokess Theorem Jo ellipse on

A: Given, F=x2i+2xj+z2k On the ellipse S=4x2+y2≤4,z=0 According to Stoke's theorem,…

Q: x(t)=2t? \yle)=r²–4¢ a) For -5sts5 , find all points (x, y) where the slope of this curve is zero.…

A: Part (a):   The slope of the parametric curve x = x(t) , y = y(t) represent the rate change dy/dx at…

Q: Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 4z² : =…

A: Given equation: ellipsoid: 4x2+y2+4z2=4; half-cone: y2=x2+2z2 To find: parametric equations for…

Q: to Find lagrange Muitiplier use point P (x 191Z) closest to the origion 2x +y -Z=5 .veriky .verily…

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Q: 6. What is the equation for the slope of the ellipse+= 1 at (x₁, yi)? A. B. C. D. E. y' = y' = b²y₁…

A: We have to find the equation of the slope of ellipse at the point (x1,y1).

Q: x² Q 6) Find the equation of the tangent to the ellipse y² = 1 at the point (xo, Yo)

A: To find the slope of the tangent at (x0,y0) we find dy/dx and put x=x0 and y=0 in it

Q: II. Find a parametrization for the following curve. (a) The circle centered at (2, 1) of radius 3.…

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Q: Cylinder ytZ =1 and plane X-y=0 are given. find the curve that is their intersection and specify the…

A: If we plot the curve y2 + z2 = 1, we get  and if we plot x-y = 0, we get

Q: If A, Band C are three points on the hyperbola yx = c^2 such that AB subtends a right angle at C,…

A: If A, B and Care three points on the hyperbola yx = c2 such that AB subtends a right angle at C,…

Q: Which graph shows the intersection curve, in the first octant, between a cylinder of equation: (x −…

A: In this question, we need to find the curve which describes the intersection of the surfaces.…

Q: xt=2r? yle)=r²–4¢ a) For -5sts5 , find all points (x, y) where the slope of this curve is zero.…

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Q: JT is tangent to 00 at T. Complete. 1. If OT = 6 and JO = 10, then JT = 2. If OT 6 and JT = 10, then…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: What is the definition of a parabolic cylinder?

A: The parabolic cylinder functions are the solutions to the differential equation d2ydx2 + ax2 + bx +…

Q: vn n centre upon any tangent to the ellipse + = 1. x² 1² a² b²

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Q: find the surfase area of ellipsoid obtained by yevoiving the upper-half of the ellipse…

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Q: Consider the equation uzz + 2/yuzy + tUyy = 0. Find the points in the ry-plane where the equation is…

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Q: Find the volume of the given rectangular pyrar 6 cm 10 cm 4 cm

A: Use formula to calculate volume

Q: 64. Find equations of both the tangent lines to the ellipse x² + 4y2 = 36 that pass through the…

A: Given: The Equation of the ellipse is x2 + 4y2 = 36

Q: Point P(a cosh t, b sinh t) where t is a parameter lies on the hyperbola with x² y² Cartesian…

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Q: d the distance between the point (2, -4, 3) and the plane 5x – 2y + z = 10

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Q: 4) The curve y = x²,-1<x< 0 is rotated about the y -axis. Find the surface area of the resulting…

A: The formula for calculating the surface area (say S) of the curve y=f(x) is given by:…