By differentiating implicitly, find the slope of the hyperboloid 22 + y? – 22 = 1 in the x-direction at the points (1, 2, 2) and (1,2, -2)

Q: Find the coordinates of the vertex of the parabola y = x^2 - 4x + 1 using derivatives O (2, -3) O…

A: To find the vertex of the parabola by using derivatives

Q: Find the equation of the Hyperbola whose Foci are at (6,4) and ( 30,4),and the length of its…

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Q: Find the length of a,b,c of the hyperbola: y^2-x^2=1

A: The given equation of hyperbola is: y2-x2=1

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

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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: Find the equation of the line tangent to the hyperbola x + 2xy - y + x = 5 at the point (3,7)

A: Given,            x2+2xy -y2+x =5 and point (3,7)

Q: 2. Which equation represents the parabola with focus (1, 4) and latus rectum of 4? Oy = 4(a- 1)2 + 3…

A: Here, the parabola is of the form (x-h)2=4a(y-k) Whose focus is given by (h,k+a)=(1,4) given…

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: What is the standard equation of the hyperbola if the length of its transverse axis is 12 and one of…

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Q: = 1 10 12 = 1 20 12 x2 = 1 100 36 =1 100 144

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Q: What is the equation of a parabola in standard form with vertex V(3, – 3) and focus F(3, 2)? A (x-…

A: NOTE: Refresh your page if you can't see any equations. . the vertex is at  and the focus is at

Q: By differentiating implicitly, find the slope of the hyperboloid x² + y? – 22 =1 in the x-direction…

A: Given that: x2+y2-z2=1

Q: Select a possible equation for a parabola with a vertex of (-1,3). Oy = (z + 1) (x – 3) | Oy = (z -…

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Q: Find the length of a,b,c of the given hyperbola: x^2/4 - y^2/5=1

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Q: Find the point on the hyperbola xy = 8 that is closest to the point (3,0)

A: Given: xy=8 so, y=8x now any point of given hyperbola can be written as x,8x so, let's that point on…

Q: Given hyperbola   (y + 1)2   −   (x − 2)2   = 1       9                4         what will its…

A: Given: An equation of the hyperbola, y+129-x-224=1.

Q: Find the equation of the tangent to the hyperbola x2 - 4y2 = 9 at (5, 2).

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Q: What is the equation of the line tangent to the hyperbola = 1 at the point (V2a, b)? y = -a+b 26 V26…

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

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Q: The parabola y2 =-14x has it's focus at the point (b,0) where b is?

A: The standard equation of parabola for this condition is y2=-4ax here  Focus (-a, 0)   Now, we have…

Q: What is the equation of the ellipse with the center at (0.0) that passes through the points (2,0),…

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Q: It is true that the vertex is halfway between tje focus and the directrix on the principal axis

A: Yes, the vertex is halfway between focus and the directrix on the principle axis

Q: Find the equation of the Hyperbola whose Foci are at (6,4) and ( 30,4).and the length of its…

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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: 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: What is the equation in standard form of an ellipse whose center is at C(-3, 1), a vertex at V(-5,…

A: NOTE: Refresh your page if you can't see any equations. . the standard form of the ellipse is given…

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: Find an equation of the parabola that satisfies the conditions. a) Focus (0, -) and directrix, y =…

A: Given  Focus (0 , -1/2)  Directrix ,y = 1/2   Equation of parabola with focus at (x0 , y0) and…

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: 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: What is the equation of the line that contains the vertices of the hyperbola (z+ 4)2 (y+2)² = -1? 16…

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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: 2. Determine the orthogonal trajectory of the family of hyperbolas y² – 121x² = c. c. Sketch some of…

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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 the equation of the ellipse whose foci are at (2,1 ) and ( 6,1),and the length of its major…

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Q: Find the equation of Parabola and Graph with the following information: Center at (0, 0) Vertices…

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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: 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: Identify the type of conic section from the equation: y^2 - 4y - x^2 6x =12

A: We have been given the equation  y2-4y-x2+6x=12

Q: Find an equation of the paranola in standard form: with the vertex at V (2,-4) and directrix y= -5

A: Find an equation of the parabola in standard form: with the vertex at V (2,-4) and directrix y= -5

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: What is the equation of the directrix of a parabola having vertex at (4, 3) and focus which is 2…

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Q: Determine the type of conics for each equation using the discriminant. 27. y2-x-10y -3 0 28. x2-2y2…

A: Solution is given below:

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: 2. Which equation represents a parabola with vertex (4,4) and directrix y = 2? Oy=2x² - 4x + 4…

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Q: find the orthogonal trajectory of family of parabolas represented by the equation…

A: To find orthogonal trajectories of  y2=4ax.

Q: Find the orthogonal trajectory for the family of parabolas with center at the origin and focion on…

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Q: Find the equation of the horizontal ellipse that is centered at ( 15, 10), passes through the point…

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Q: The equation of the hyperbola whose foci are (-2,0) and (2,0) and length of transverse axis is 2 is…

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