2. Find the equation of the parabola with focus (2, 0) and directrix x = -2. а. b. x' = 8y c. y = 8x d. x = -8y

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

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Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 1) and directrix…

A: Given that Focus of parabola is F0, 1. Directrix is y=-1. We have to prove that y=14x2 is the…

Q: Find the family of curve that intersects the family of hyperbolas y² = 2x² +b at an angle arctan(1).

A: To find the family of the curve that intersects the family of hyperbolas y2=2x2+b at an angle…

Q: b) Consider now the portion of the parabola which is below the line y = 2. Which points have the…

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Q: Find the equation of the line tangent to the ellipse x + 3y 19 at the point (4,1). (Type an…

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Q: 1. Find the equation for the parabola that has its vertex at the origin and has directrix at y = 25…

A:

Q: Find a parametrisation of the hyperbola that is obtained by translating the hyperbola with equation…

A: Here we need to find the effect of translation on parametric equation of hyprabola.

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

A: According to the given information, it is required to find the maximum and minimum value of the…

Q: The equation x2-xy+y2=1 describes an ellipse. Find the coordinates (x,y) of all the points on the…

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Q: Find the equation of the conic section indicated. Parabola with focus (8, 0), directrix x = −8

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Q: Determine the eccentricity of a hyperbola with a vertical transverse axis of length 48 units and…

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Q: Find the equation for a hyperbola centered at (0, 0), with foci at (0, - V 52 -6) and (0, 6). y? x2…

A: Here we have to find the equation of hyperbola having a center (0,0) with foci at 0,-52 and 0,52 and…

Q: Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (1, 0). (x,y)=(?)…

A:

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

A:

Q: Find the point(s) on the hyperbola x^2 - y^2 = 2 closest to the point (0, 1).

A:

Q: Find the equation of parabola with rertex at (0,0 and focus at (3

A: Given the vertex is at(0,0) and focus (3, 0)

Q: 2. Determine the orthogonal trajectory of the family of hyperbolas y? – 121x? = c. Sketch some of…

A:

Q: Derive the equation of the parabola with a focus at (6, 2) and a directrix of y = 1. 1 O f(x) = -- 2…

A: We can derive the equation of parabola as below.

Q: Find the evolute of the parabola y=x2.

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Q: Given hyperbola   x2   −   y2   = 1   9         16       how do you determine the focal length?

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Q: Determine the area of the largest circle that can be enclosed by the two hyperbolae, xy= 1 and xy =…

A: Solution is here

Q: 1 Find the equation for the parabola that has its vertex at the origin and has directrix at y 27…

A: Given: y=-127.

Q: How far from the x axis is the focus of the hyperbola (x^2)- (2y^2) + 4x + 4y+ 4 = 0?

A: the given equation of hyperbola is  x2- 2y2+4x+ 4y + 4 =0 it is asked to find how far is focus of…

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: 3. Find an equation of the hyperbola having foci at (4, 3-V 52) and (4, 3 +/52) and asymptotes at y=…

A: Focii: (4, 3+52) & (4, 3-52)Assymptotes : y=3x2-3 , y=-3x2+9Let vertex by represented by (h,k)…

Q: 14. Evaluate [4x dæ + 5y“ dy if C is the portion of the ellipse 3x2 + 7y? = 21 in the first…

A: Explanation of the solution is given below....

Q: Find equations of both the tangent lines to the ellipse  x2 + 7y2 = 63  that pass through the point…

A: consider (x0 ,y0) be an any point on ellipse

Q: Find the point (x, y) on the ellipse, 4(x - 1)^2+ y^2 = 1, that is farthest to the origin (0, 0).

A:

Q: Find the standard form of the equation of the ellipse with the given characteristics. y 1아 (7,8) 8…

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Q: The orthogonal trajectory of y= Ce" is a parabola of the form y = ax+b. what is the value of b so…

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Q: 6. x2 + y² + 4x - 10y - 52 = 0 O Cirde O Ellipse O Hyperbola O Parabola

A: Given: The equation of the conic is  x2+y2+4x-10y-52=0   To determine: The type of the conic from…

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

A:

Q: Find the equation of the surface of revolution generated by rotating the parabola y = z^2 around the…

A: A surface of revolution generated by rotating a curve described by y=f(z) around z-axis is given as…

Q: Find an +y² equation for the tangent to the ellipse 4 = 2 at the point (2,0).

A: Consider the ellipse, x24+y2=2

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A:

Q: . The general form of equation of an ellipse is given by Ax + Cy + Dx + Ey +F = 0, where A and C are…

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Q: B. Find the general form of the equation of the parabola: 1. With focus Fat (2,7) and directrix e: y…

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Q: 28. Find the directrix for the parabola. (y+ 3)2 + 8 2x x = 4 y = } 7/2

A:

Q: Find the equations of the normal and the tangent to the hyperbola xy + 2x - 5y-2= 0 at the point (3,…

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Q: 1 in (r', y')-coordinates, if (iii) Find the equation for the hyperbola ry 0 = 1-

A: Find the equation of hyperbola in x'y' system

Q: By differentiating implicitly, find the slope of the hyperboloid 22 + y? – 22 = 1 in the x-direction…

A: We have to find slope of the hyperboloid x2+y2-z2=1 in the x-direction at the points (a) 1,2,2 (b)…

Q: If a person shoots a basketball overhand from a position 8 feet above the​ floor, then the path of…

A: The path of the basketball through from the hoop is modeled by the parabola,

Q: 4x^2 + y^2 = 4 that are the farthest away from point (1,0)

A:

Q: Find an equation of a parabola with focus at (−2,0) and with directrix x=9(Express your answer in…

A: Given that the parabola has the following details:

Q: which satisfies th

A: Parabola: The focus of the parabola is (-2,-5) The directrix x=6 The general form of parabola is…

Q: 1 Find an equation of the hyperbola having foci at (5-/45, 0) and (5+/45, 0) and asymptotes at y = 5…

A:

Q: Find the equation for the parabola that has its vertex at the origin and has directrix atI = 27…

A:

Q: 12. Determine the equation of the directrix for the parabola 20x=y2–10y+30 а. X-20 b. y=-20 с. X3-20…

A: Question : Determine the equation of the directrix for the parabola 20x = y^2 - 10y +30.

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.