By differentiating implicitly, find the slope of the hyperboloid x² + y? – 22 =1 in the x-direction at the points (1, 4, 4) and (1,4, – NOTE: Enter the ezact answers. The slope at the point (1,4, 4) is

Q: 3. Find the coordinates of the foci of the ellipse given by the equation 4x² + y? = 64. O (0, 4v3)…

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Q: Find the equation of the parabola with a focus at (1, -8) and a vertex at (1, - 2). Let a represent…

A: Since the x-coordinates of the vertex and focus are the same, they are one of top of the other. So,…

Q: Use the Distance Formula to write an equation of the parabola with focus F (0, – 11) and directrix y…

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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: An insect is tracing an elliptical boundary of a hot plate. The ellipse equation is given by+ = 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: 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: Find the equation of tangent lines to the ellipse parallel to the line y =3. The equation of ellipse…

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Q: Which of the following equations represents the parabola with vertex at (3, 2) and directrix y = 4?…

A: To find out the equation of the parabola.

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: 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 maximum and minimum values f(x, y) = xy can take on the ellipse 4.x?+y? = 16.

A: Here we have to find maximum and minimum value of given function.  The solution is in 1st and 2nd…

Q: Find the equation of the asymptote with a positive slope for the following hyperbola. (x + 8)? 1 (y…

A: Given hyperbola s standard equation of hyperbola : Therefore,

Q: Determine the standard equation of the ellipse. Foci at (-3,4) and (7,4); vertex at (-9,4) Choose…

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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 equation of the ellipse with foci and 0, and vertices (0, - 2) and (0,2). O x? y2 1 4 %3! O…

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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: Which point or points on the ellipse x? +4y? = 4 are furthest away from the point (0, 1)?

A: The Equation of the given ellipse is, x2+4y2=4 Let the furthest away point on the ellipse, from the…

Q: find the equation of the parabola y = ax? + bx + c that passes through the points. (0, 3), (1, 4),…

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Q: Find the equation of the Hyperbola whose Foci are at (7,9) and ( 35,9),and the length of its…

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Q: The parabola y=x^2+13 has it's focus at the point (b,c) where  b= c=

A: The given equation of the parabola is, y = x2+13. Also the parabola has its focus at (b, c).Consider…

Q: Find the points on the ellipse 25x? + y² = 25 that are farthest away from the point (1, 0). List all…

A: Given equation of ellipse, 25x2+y2=25So, y=±25-25x2 Now distance between the points (x,y) and (1,0)=…

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

A: topic - conics

Q: Find b and c, given that the parabola y = x2 + bx + c passes through (0, 5) and (3, 23).

A: (0,5) means when x=0 then y=5. similarly, (3,23) means when x=3 , then y=23.

Q: Find the equation of the ellipse whose foci are at (7,3) and ( 21,3),and the length of its major…

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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: 3. Find the equation of the parabola with focus at F(3,2) and with the line x = -4 as directrix.

A: Topic- equation of parabola from focus ans directrix.

Q: Find the standard form of the equation of the hyperbola satisfying the given conditions. Endpoints…

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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: Find the standard form of the equation of the parabola satisfying the given conditions: Focus :…

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Q: find the points on the parabola y=x^2 closest to the point (0,1)

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Q: Find an equation of the parabola that satisfies the given conditions.Focus F(2, 0), directrix x = -2

A: If the coordiantes of the focus h+p,k and directrix x=h-p Then, equation of parabola y-k2=4px-h We…

Q: find the equation of the parabola with the given  Focus (2, 0), directrix x = −2

A: Our Aim is to find the equation of the parabola with the given Focus (2,0) and directrix x=-2.

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

A: Solution Given V=(0,0)F=(a,0)=(5,0)To find the equation of the parabolaFormula:y2=4ax

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: 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 extreme values of f(x, y) = e¬¤y for the points on the ellipse x² + 4y? = 1

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Q: Find the equation for the ellipse with foci at (-1,3) and (5,3) and whose minor axis has a length of…

A: Given:- The ellipse with foci at (-1,3) and (5,3) and whose minor axis has a length of 4 units. To…

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 an equation of the parabola that satisfies the given conditions.Focus F(6, 4), directrix y = -2

A: Given: Focus F(6,4) directrix y=-2 To find: the equation

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: Find an equation of the parabola with focus (4, 4) and directrix x=0.

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Q: Write the reduced hyperbole equation, given: a) The foci ( ± 5.0), and the length L=9/2 of the rope…

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Q: The parabola has focus (0,-2) and directrix y=2.

A: equation of parabola with focus ( a , b ) and y = c  is given as below : here a = 0 b = -2  c = 2

Q: Find an equation of the parabola that satisfies the given conditions.Focus F(-3, -2), directrix y =…

A: We have given the equation of directrix is y=1 which parallel to the x-axis. The standard equation…

Q: Find all values of b such that the parabola y = x² – bx + will have a directrix having an equation…

A: y=18x2-bx+92 On simplification, we get…