Evaluate –dz , where C is the ellipse 4x² + 9y? = 1. %3D Yc z2 – 3z+2

Q: What are the foci of the ellipse? 49 42 O (2+ v7, 1) o (2+ 7, -1) o (tyī, 1) o (12/7, - 1)

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Q: Find the largest and smallest values that the function ƒ(x, y) = xy takes on the ellipse x2/8 + y2/2…

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Q: What is the equation of a parabola with focus at (2,6) and directrixx = 8? %3D O y - 12y + 12z – 24…

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Q: Find the value of Y for the hyperbola defined by the equation y² – x² = 7 at the point (3, 4). dx2

A: The equation is y2-x2=7. First find the value of dydx as follows.…

Q: 4. §yʻ dz + 2ry³ dy, where C is the ellipse z + 2y? = 2.

A: To Determine: find the integral  Given: ∮y4dx+2xy3dy where C is the ellipse x2+2y2=2 Explanation: we…

Q: the area of the ellipse 9x^2 + 8y^2 = 72 answer: 26.7

A: To Find: Area of the ellipse  9x2+8y2=72

Q: Find the maximum and minimum values of the function f(x, y) = xy on the ellipse given. y? by the…

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Q: Find the perimeter of the ellipse x2/a2 +y2/b2 = 1, where a > b > 0.

A: The perimeter of Ellipse with Radii a and b is given by: In our question the radii is a and b Hence…

Q: (d) If x + y = xy, show that y" = . (e) Evaluate y" for the ellipse b'x? + a²y² = a²b°.

A: We have to differentiate the given expressions with respect to x.

Q: Scalar line integrals Evaluate the following line integral along the curve C.

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Q: y? = t2 – 2t and x = t + 2 is I. Ellipse II. Circle III. Parabola IV. Hyperbola

A: topic - conics

Q: 6. What is the equation for the slope of the ellipse+-1 at 1 at (x₁, ₁)? A. B. C. D. E. y' = -21 y'=…

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Q: for the ellipse 4x^(2) +y^(2) +24x -2y +21 = 0, find its area

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Q: Find the points on the ellipse  X^2 + 6y^2 + 3xy =40 With the greatest x coordinator

A: Let us assume thatfx,y=xandgx,y=x2+6y2+3xy-40The lagrange multiplier equations…

Q: Write the equation of the ellipse 4x + 9y² + 72x + 108y + 612 = 0 in standard form. O (*+9)² +…

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Q: find the perimeter of the ellipse x2/a2 + y2/b2 = 1.

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Q: 1. Find the minimum and maximum values of f(x,y) : = x²y on the ellipse 4x? + 9y? = 36. %3D

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Q: x² y²=1? What is the area of the ellipse: + 36 16

A: For the calculation of area of ellipse,

Q: F. dr, where C is the ellipse (x + 3)² + 5(y – 2)² = 16 and F(r, y, z) = x²i +y²j+ z²k.

A: The vector field is Fx, y, z=x2i+y2j+z2k. The curve C is x+32+5y-22=16. Obtain the parametric…

Q: Match the ellipsoids shown in the table with the equations. Answer Bank x2 + 2y2 + 2z² = 4 2x2 + 2y?…

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Q: Prove that evolute of the ellipsé x2 y? = 1 a? b2 is (ax)2/3 +(by)2/3 = (a² – b²)²/3. %3D

A: Given equation of the ellipse be x2/a2 + y2/b2 = 1 Write the equation of the ellipse in parametric…

Q: Write the equation of the ellipse 4x + 9y + 72x + 108y + 612 = 0 in standard form. O (e+9)² + (y+6)°…

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Q: Find the area inside the ellipse x2a2+y2b2=1.

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Q: Find the equation of the line tangent to the hyperbola x2 −y2 =16 at (5,3).   Give your answer in…

A: The line is tangent to the given hyperbola at (5,3).Tangent line is a straight line.Therefore, the…

Q: Write the equation of the ellipse 4x² + 25y? – 40x + 150y + 225 = 0 in standard form %3D (x – h)?,…

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Q: Write the equation of the ellipse 25a? + 36y² + 150x – 72y – 639 = 0 in standard form (x – h)? (y –…

A: Wr have to write the ellipse equation in standard form .

Q: Find the coordinates of the four points at which the hyperboloid of one sheet given by x2 y? + 16 z?…

A: This question is related to 3D coordinate geometry, We will solve it using given information.

Q: Find the shortest distance from the point (o, 5) to the ellipse 3y? = x³.

A: We will find the the distance from the given problem.  We know      Distance (D) = sqrt {(x-x1)2…

Q: Find the evolute of the ellipse x2 / a2+y2 / b2=1.

A: The given ellipse has the equation:

Q: The area of an ellipse with axes of length 2a and 2b is A-πab. Approximate the percent change in the…

A: It is given that, the area of the ellipse with axes length 2a and 2b is

Q: Show that the ellipse x*/a? + y*/b? = 1 and the hyperbola x/A? – y/B² = 1 are orthogonal…

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Q: F. dr, where C is the ellipse (x + 3)² + 5(y – 2)² = 16 and F(x, y, z) = x²i+ %3D Pj+ z°k.

A: Given: x+32+5y-22=16 Fx,y,z=x2+y2+z2

Q: Write the equation of the ellipse 36æ² + 4y? + 72x + 32y – 44 = 0 in standard form (x – h)? p2 (y –…

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Q: (-3x) dxtxdy C is part of the ellipse 5x2+6y=30 fromC0,-V5) to cra,O). X,

A: Line integral Given ellipse is  From .

Q: 1 Jl جمح The ellipse (4-x) a? (y-k)? = 1 is vertical a. a > b b. a < b +

A: To find the correct option

Q: What is the area of the ellipse x² 16 + y² 9 = 1?

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Q: Find the area of the ellipse given by x2/64+y2/ 4=1. Area =

A: Solution: The objective is to find the area of the ellipse given by x264+y24=1

Q: Find an equation of the parabola deseribed. Focus at (5, 0); vertex at (0, 0) O y = 20x2 O x = 20y O…

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Q: Find the maximum and minimum values of f(x,y)=xy on the ellipse  4x^2+y^2=6

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Q: Find the minimum and maximum values of f(x, y) = x2y on the ellipse 4x2 + 9y2 = 36.

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Q: Write the equation of the ellipse 9a²+ 16y² – 90x – 32y + 97 = 0 in standard form a2 (x – h)? (y –…

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Q: Q9: Show that in an ellipse b2 = a² (1 – e? ).

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Q: Given the ellipse x^2/16+ y^2/4=1. What is the area of the largest rectangle that can be cut from…

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Q: Answer the following True or False: (x + 1)² Let (y + 8)? + + 8)? = 1 a2 62 be the equation of an…

A: SOLUTION: (x+1)^2/a^2+(y+8)^2/b^2=1 center=(-1, -8) but in question given center=(1,8) hence false

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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Q: Find the area enclosed by the ellipse (x2/a2) + (y2/b2) = 1

A: Consider the given equation as x2a2+y2b2=1

Q: What is the equation of normal to the ellipse 9y^2 + 4x^2 = 25 at (2,-1) ?

A: Slope of normal is -dx/dy  So we differentiate both sides with respect to x Then we plug x=2 and…

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.