At what points does the curve r(t) = t i + (6t - t2)k intersect the paraboloid z = x2 + y2? (Enter your answers from smallest to largest x-value.)

Q: Find the points on the ellipse x2+2y2=1, where f(x,y)=xy has its extreme values.

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Q: 7. A curve in the zy-plane is described by the equation 2y(x − 1)² – xy² + 1 = 0. (a) Determine…

A: Given equation of curve: 2yx-132-xy2+1=0 Now, from the given points (1,0) , (2,0), (1,1) , (2,1) and…

Q: Find the maximum and minimum values of the function f (x,y) = 2x² – y² on the ellipse p² + 2 (y –…

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Q: Find the coordinates of the intersection points A and B, between the closed curve (x + 1)² + 4(y-1)²…

A: In this question, we can find the intersection points of the given curve. Using the equation of…

Q: "What is the families of the curve of all Parabolas with axis parallel to the x-axis

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Q: Do the curves ri(t) = (t² + 3, t+1, t² – 5) and rž(s) = (4s, 2s – 2, s + 1) intersect? If so, at whi…

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Q: Find the points of intersection of the curves. Then sketch their graphs on the same Cartesian plane.…

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Q: An aircraft flies along the route C defined parametrically by the equations 4 1 x = 2t, y=-t 2²…

A: An aircraft flies along the route C defined parametrically by the equations where x , y , z are in…

Q: 7. For the parabola 4x + 2y² + 8 = 0, fine the directrix. (a) y = x = (C) 3 N|WN| W | 2 (b) (d) x =…

A: Given query is to find the directrix of the parabola.

Q: 2. Consider the equation r = 4 – y². (a) Find a parameterization of the segment of this parabola…

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Q: The equation of a quadratic relation is y = -(x - 1)² +3. Every point on this conic is equidistant…

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Q: enter-radius form of the equation of t

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Q: A parabola has a focus of F(2,−0.5)F(2,−0.5)and a directrix of y=−1.5y=−1.5. P(x,y)P(x,y)represents…

A: Let (x, y) be any point on the parabola. So, the distance between (x, y) and the focus will be :

Q: Solve the problem. Find the point on the parabola z = t, y = t, -00 <t <o, closest to 9 3 A) ) %3D…

A: Here we will use the concept of maxima and minima. Since we will have to find out closest point to…

Q: Estimate zx (0.50, 0) and zx (0, 1.0) and zy (0, 1.0) from the contour diagram for z (x, y) in the…

A: z(0.50,0) = 1z(0.75,0) = 2z(0.50,1) = 1z(0,1) = 1z(0,1.2) = 3z(0,1) = 1

Q: x* +4x-8y+36 = 0

A: As per guidlines i can solve only one question

Q: A parabola is defined as being the locus of points P(x, y) that satisfy FP= MP, given coordinates…

A: Formula of the distance of two points x1,y1 and x2,y2 is: d=x1-x22+y1-y22 Here, FP is the distance…

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.