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

Q: ind the equation for the tangent plane to the surface z = In(6x2 +9y2 + 1) at the point (0,0, 0).…

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Q: Find the points on the surface 1x? + 3y2 + 5z2 = 1 at which the tangent plane is parallel to the…

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Q: Find an equation of the plane tangent to the following surface at the given points. zexy; (1,0,1)…

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Q: Find the surface area of the portion of the paraboloid given by the equation z = 1– x2 – y² that is…

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Q: Suppose that a cylindrical container of radius r and height L is filled with a liquid with volume V…

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Q: snip

A: Except for degenerate cases, the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 defines an ellipse if ____.

Q: Find an equation of the tangent plane to the surface given by z² – 2x2 – 2y? = 12 at the point (1,…

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Q: find a parametrization for the curve. the left half of the parabola y = x^2 + 2x

A: First, we will find the symmetric line of the given parabola y=x2+2x. We know that the symmetric…

Q: 3. Prove that the equation of the normal to the rectangular hyperbola xy = c² at the point P (ct,)…

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Q: z = In (x² + y²) at point Po(1,0, 0).

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Q: Use the parametric equations of an ellipse, x = a cos 0, y = b sin 0, 0 < 0 < 2m, to find the area…

A: Given Parametric Equation of ellipse  x=acosθ and y=bsinθ ,0≤θ≤2π To find the area of the Ellipse

Q: Match the ellipsoids shown in the figure above with t 1) x2 + 4y + 4z? = 16 2) 4x2 + y +4z? = 16 3)…

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Q: 2 Find pxV 1+ 3x² dr, where P is the ellipse parametrized as follows: r(t) = , 0<t< 2n

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Q: Find F. dr, where F(x, y) = (xy² + cos x)i+(x²y+sin y)j and C is the ellipse C x2 + 2y2 = 9,…

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Q: Find the points on the surface 2a2 + ly² + 522 = 1 at which the tangent plane is parallel to the…

A: We will use the following method for finding the two required point.

Q: Are there any points on the hyperboloid r2 - y? – 22 = 1 where the tangent plane is parallel to the…

A: Given hyperboloid ;    x2-y2-z2=1  and equation of plne which is parallel to tangent plane  x+y-z=0

Q: Consider the curve in the xy plane defined by the equation 4y? – 22 – 8y – 6x = 21 Show that this…

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Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

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Q: For which point y on the ellipsoid æ² + 2y² + 4z² =1 (shown below) is %3D the quantity x+ y+ z as…

A: Lagrange's Multiplier:- To find:- Extreme values of f(x, y, z)…

Q: Find the equation of the plane tangent to the surface of Z= x2+ Y2 at point P(125)

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Q: Find an equation of the tangent plane to the surface 4x^2 + 9y^2 − z^2 = 14 at P = (2, 1, 4).

A: Given,4x2+9y2-z2=14at P=(2,1,4)

Q: Find the equation for the tangent plane to the surface z = - 9x - 7y at the point (2, 1, - 43). O A.…

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Q: Find an equation for the tangent plane to the surface 2° – ay? = 0 at the point (27, 1, 3).

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Q: Find the equation of spheres passing through the circle x+y+z'-6x-2z+5 =0, y = 0 and touching the…

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Q: Are there any points on the hyperboloid x 2 − y 2 − z 2 = 1 where the tangent plane is parallel to…

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Q: Find the point on the ellipsoid x2 + y2/4 + z2/9 = 1 for which x + y + z is largest.

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Q: Calculate | [(a* – 3y) dæ + (2y³ + 4x) dy] wherein y(t) = (3cos(t), 3sin(t)), 0 <t < 2ñ, is an…

A: Please check step 2 for the solution.!

Q: Prove that the product of the perpendicular distances F1R1 and F2R2 from the foci to a tangent line…

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Q: Use the parametric equations of an ellipse, x = a cos(0), y = b sin(0), 0 s 0 s 2T, to find the area…

A: Given: Use the parametric equations of an ellipse, x = a cos θ, y = b sin θ, 0 ≤ θ ≤ 2π,  to find…

Q: At what points does the curve r(t) = ti + (3t - t2)k intersect the paraboloid z = x2 + y2? (If an…

A: Given- r(t)=ti^+(3t-t2)k^z=x2+y2 To find the intersection point of the given curve and paraboloid.

Q: Need some help with Greens Theorem and ellipse plz, thanks

A: It is required to calculate the value of the integral using green’s theorem:

Q: Find the equation for the sphere centered M(2,-3,2) tangent to the D:6x-3y+2z-11=0 plane

A: we have to find the equation for the sphere centered 2,-3,2 and tangent to the plane 6x-3y+2z-11=0.

Q: Find the points on the surface 2a2+ ly? + 522 = 1 at which the tangent plane is parallel to the…

A:

Q: Determine the equation of the normal line to the hyperbola x - 4y- = 9 at (5, 2). 8x + 5y – 50 = 0…

A: Given equation of hyperbola is  x2-4y2=9          ...(1) We have to find the equation of the normal…

Q: Find an equation of the plane tangent to the following surface at the given points. z =6 cos (x- y)+…

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Q: Find the equation for the tangent plane to the surface z= In (7x + 10y + 1) at the point (0,0,0).

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Q: Find symmetric equations for the tangent line to the curve of intersection of the paraboloid zx +y…

A: Given  The equation of Paraboloid Z=x2+y2 The equation of Ellipsoid 2x2+y2+z2=76

Q: find a parametrization for the curve. the lower half of the parabola x - 1 = y2

A: Consider the given equation x - 1 = y2 By adding 1 from both sides, ⇒ x = 1 + y2 Let, substitute y =…

Q: Find the curvature of the parabola f(x)= ax +bx+c at its vertex 2a ’

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

A:

Q: At what points does the curve r(t) = ti + (6t – t2)k intersect the paraboloid z = x² + y2? (If an…

A: Given, r(t)=t i +(6t - t2)k ......(1) and z=x2+y2 .......(2)

Q: Are there any points on the hyperboloid x² – y² – 2² = 1 where the tangent plane is parallel to the…

A: By see this solution

Q: The tangent plane to the elliptic paraboloid z = -2x - 7y? at the point (-3, -4) is

A: Consider the provided question, The equation of the tangent plane to the elliptic paraboloid at the…

Q: Find the point closest to the origin on the curve of intersection of the plane 2y + 4z = 5 and the…

A: We have to find the point closest to the origin on the curve of the intersection of the plane…

Q: Find all points on the ellipsoid 2r² + 3y² + 4z² = 9 at which the plane tangent to the ellipsoid is…

A:

Q: 12. Let H be the hyperboloid where x² – y² + z² = 6. Find an equation for the tangent plane to H at…

A: As you asked only solution for Q12 so, I answered here only Q12

Q: What is the maximum height of a particle whose path has parametric equations x = t9, y = 4 − t2?

A: The height of the particle is given by it's y position: y = 4 - t2 At the maximum height, dy/dt = 0

Q: Are there any points on the hyperboloid r² – y² – 2² =1 where the tangent plane is parallel to the…

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Q: Find any points on the hyperboloid  x2 − y2 − z2 = 6  where the tangent plane is parallel to the…

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Q: Find a parametric description for the ellipse 9x^2+4y^2+24y=0, oriented clockwise and where t=0…

A: Given equation of the ellipse 9x2+4y2+24y=0.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.