Derive the equation of the parabola with a focus at (6, 2) and a directrix of y = 1. 1 O f(x) = -- 2 3 O fx) = -x - 6) + 2 3 - (x – 6)² + 2 f(x) = O f(x) = -(x + 2 + 6 2 (x + O f(x) = 2 %3D

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

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Q: 14. Find the maximum and minimum values of the function f(x,y) y? = xy on the ellipse given by the…

A: Given f(x,y)=xy subject to    g(x,y)=x2+y24-1=0 We have to find the maximum and minimum values of…

Q: Give the equation of the parabola with focus F (0; 2)  and directrix y = -2 . Give an equation of…

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Q: Find a function whose graph is the lower half of the hyperboloid -x2 - y2 + z2 = 1.

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Q: There is a parabola which has a minimum where the two lines 3x+6y-1=0 and 2x+ y-2=0 intersect. The…

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Q: Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = -1. f(x) 4 O (x) =…

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Q: 2. The orthogonal trajectory of y = ce" is a parabola of the form y = ax+b. Find the values of a & b…

A: See the details solution in below

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: Derive the equation of the parabola with a focus at (-7, 5) and a directrix of y = -11. O (x)= (X +…

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

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Q: 3. Determine the orthogonal trajectory of the family of parabolas x² – y + 32x = 0. %3D Sketch some…

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Q: Find the equations of asymptote lines of the hyperbola y-x +14 x-8 y 37 Select one: O None Oy = +…

A: Given, y2−x2+14x−8y=3 To find the equation of  asymptote do as follows.

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

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Q: Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8. 1 O f(x) -(x –…

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

Q: The orthogonal trajectory of y=cex is a parabola of the form y2=ax+b. Find the values of a and b so…

A: See the details solution in below

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: 5) Find the equation of a parabola with focus F(7/2,3) and directrix line ==1/2. *

A: We shall use focus-directrix property to solve this problem. This property says, the distance…

Q: Find an equation of the ellipse with foci at (−3,7)and (−3,−3) and whose major axis has length 20.…

A: The foci of the ellipse is (−3,7)and (−3,−3). The length of the major axis is 20.

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: The standard equation of the parabola is given as y2=4ax . This parabola has symmetry about the…

Q: Determine the standard form of equation of a hyperbola with foci at (-1,0), (1,0) and one of its…

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Q: 2. Suppose that the equation Ax + Bxy + Cy² + Dx + Ey + F = 0 represents a conic section…

A: The equation Ax2+Bxy+Cy2+Dx+Ey+F=0 represents a conic. If B2-4AC>0 , The conic represents…

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

A: We have the given function is f(x,y)=xy    ..... (1)   The equation of ellipse  x2+y24=1 Let…

Q: The function of f(y) is a "sideways" parabola with a standard equation of SW) = ay² + by + c, f(G)…

A: Given: Focus of Parabola:  (2, 6) Equation of Directrix:  x = -15

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: Sketch the parabola y = x² + 2x +1. Use arrows to indicate the maximum and minimum values of y over…

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Q: Show that the ellipse 4x + 9y = 45 and the hyperbola x - 4y = 5 are orthogonal %3D

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Q: Find the maximum and minimum values of the function f(, y) = xy on the ellipse given %3D y? by the…

A: Given :  The function f ( x, y ) = x y and the ellipse  x2 + y24 = 1.   To determine :  The maximum…

Q: Find the y-intercept and any x-intercept(s) of the parabola with equation y = -(x + 7) + 16. If the…

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Q: 14. Find the maximum and minimum values of the function f(x,y) = xy on the ellipse given %3D by the…

A: Let f(x,y)=xy subject to     g(x,y)=x2+y24-1=0 We want to find extreme values of f(x,y)=xy on the…

Q: The orthogonal trajectory of y= ce" is a parabola of the form y ax+b. Find the values of a & b so…

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Q: 1. Determine the foci, vertex, and directrix of the parabola with the given equation. (a) x2 = 10y…

A: Dear learner, as per our guidelines , g can solve only 3 subparts of one questionat once. Further…

Q: Find the directrix for the parabola. y = 20 (x+ 2)² - 3 1- x= -1 O y = -1 O y = -8 y 3= O x = -8

A: We will find out the required equation of directrix.

Q: 9. Find an equation of the hyperbola whose transverse axis is horizontal, with center at (2, –2) and…

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Q: 4. Determine whether a hyperbola exists if it has an equation of x2 - y2 + 6x +36y = 18.

A: we have to determine whether a hyperbola exists if it has an equation of  x2-y2+6x+36y=18

Q: Find the equations of asymptote lines of the hyperbola y-x2+ 14 x-8y 37 Select one: O None Oy =…

A: Given, y2-x2+14x-8y=37

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: 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: 17. Let f(x, y) xy. Find the minimum and maximum values on the ellipse x² + 4y² = 4.

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Q: Find the maximum and minimum values of f(x, y) = 7x + y on the ellipse x2 + 9y² = 1

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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: The parabola y + 2y + 8x –7=0 has vertex at O (-1, –1) o (-1,1) о (1,-1) о (1,1)

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Q: 9. Find an equation of the parabola that satisfies the given condition: Vertex V(-1,0) and focus…

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Q: Picture of question is attached.

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Q: Given a hyperbola with the implicit equation: (y – 2) (x +2)² %3D 9. 25 Choose BOTH slopes of its…

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Q: Find the equations of asymptote lines of the hyperbola y-x2+14 x - 8 y = 37 Select one: O None…

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

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Q: 5. The hyperbola x? y2 1 has a horizontal transverse axis and 2 asymptotes %3D a2 b2 y = +x.

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Q: 6. Find the parabola y = ax² + bx +c passing through the points (–2, –6), (1, 6), and (3, 4).

A: Lagrange polynomials are used for polynomial interpolation. For a given set of distinct points xn…

Q: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex…

A: Finding the equation of parabola