Prove that at (x, y, z) the point of intersection of three confocals +² y² and + b- + -x-² a² + H he osculating plane of the curve = 1 + 1,² z² + 6² +μ c² +μ = 1, Σ a² + 2 a² + 2) + of intersection of the first two is given by ¸x x¡₁ (a² + µ) a² = 1 + b² +2 c²² +2 = 1

Q: An equation for the tangent plane to the surface : = (xty at the point P(1, 1, 4) is a) 8x + 8y -: =…

A: Equation of a tangent to the surface z=f(x,y) at point (a,b,f(a,b)) is given by…

Q: 4) Show that the surfaces 3X² + 2Y²+Z² = 9 and x² + y² + Z²-8X-6Y-8Z + 24 = 0 have a common tangent…

A: We have to prove both surfaces have common tangent at P(1,1,2).

Q: Find the tangent plane (Xo, Yo, Zo) from f (x, y) = x² - 3y²; (0,1, -3)

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Q: What is the length of the part of the curve y squared = (x-1) between the points (1,0) and (2,1)?

A: To find- Length of the part of the curve.

Q: Find the equation of the tangent line to the curve 3 x' + 2 y – 22 = 3 xy – x at the point (2, 2).…

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Q: The tangent plane and the normal line of the surface y = x² + z – 6 at the point (2, -1, 1) have the…

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Q: The equation of the tangent plane of the graph of function z = xy + 2x² - y3 at point (2, -1) is

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Q: B) r(t) = (4 cos t, 4 sin t, 16)

A: We consider x=rcos(theta) and  y=rsin(theta)  Therefore r^2=x^2+y^2

Q: Suppose that the plane tangent to the surface z = f(x, y) at (-4, 2, 5) has equation z + 5x + 4y =…

A: From the equation of tangent, we can derive: z = -(7 + 5x + 4y) Hence,

Q: Integrate h(x, y) = (x+y)i + (y²-x)j over the closed curve that begins at (-7,0), goes along the…

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Q: An equation for the tangent plane to the surface (xty at the point P(1, 1, 4) is a) 8r + 8y-:= 0 b)…

A: The given surface is  f(x,y)=z=(x2+y2)2  ...........(1); we have to find the tangent plane at point…

Q: Where does the plane tangent to z = At z = 5exy at (7, 7, 5) meet the z-axis?

A: We find equation of tangent plane to z=5e^(x-y) at (7,7,5)

Q: The Normal line at the point (0, –1, 1) to the 3 surface exy - xy² + z³ = -2 is 7=y+1=² Select one:…

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Q: 3) . (3x2 — Зуz+ 2xz)dx + (3у? - 3xz + z?)dy + (372 — Зху + х? + 2yz)dz Calculate the curvilinear…

A: Let's find.

Q: Evaluate ∮C (x + 3y)dx + ydy where C is the Jordan curve given by the graphs of y = e^x, y = e^−x…

A: ∮Cx+3ydx+ydy Where C:y=ex, y=e-x, y=e-1

Q: The tangent plane to the surface 2x² + 3y² = 5z² at (1, 1, 1) has an equation ax +by+cz = d.What is…

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Q: The equation for a plane tangent to z = f(x, y) at a point (xo, Yo) is given by z = f(xo, Yo) +…

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Q: Find the distance from the point S(0,0,0) to the plane 20x+10y+5z=70 (approxmate to two decimal…

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Q: Find the equation of the tangent plane to the sphere x² + y2 + z² = 1 at the point (1/ V3, 1/V3, 1/…

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Q: x ds, where C is the portion of the parabola from (0,0) to (1, 1), followed by the line segment from…

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Q: Find the equation of the tangent plane to the surface of the equation z = x2 + y2 - 2xy on the point…

A: Equation of tangent plane

Q: TRUE OR FALSE? The given line integral is independant of path.

A: The given line integral is ∫C2xz3+6ydx+6x-2yzdy+3x2z2-y2dz Compare the above line integral with…

Q: drawn from the point A(2,10) on the parabola y = x^2 + bx + c Since the tangent is parallel to y =…

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Q: ) Find the points on the ellipsoid 6x² + y² + 3z² = 4 where the tangent plane is parallel to the…

A: