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

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

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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: Find the standard equation of the hyperbola. Two corners of auxiliary rectangle at (−4 ,−7) and (0…

A: Given: The two corners of the auxiliary rectangle of a hyperbola are at -4,-7 and 0,0 and transverse…

Q: Determine the greatest and least distance from the origin to a point on the ellipsoid 9x2+4y2+z2=36

A: Here is the solution of the given problem. Application of Lagranges Multiplayer.

Q: Determine the orthogonal trajectories of the hyperbola 3xy= 5 at the point (2, 5/6). Sketch the…

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Q: Find an equation of the hyperbola that has foci at (-13,0) and (13,0), and asymptotes y=3/2x and…

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Q: Find the equation of the hyperbola with center (o, o), a vertex at (5, o) and an extremity at (o,…

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Q: Find the points on the ellipse 4x + y² = 4 that are farthest away from the point (1, 0). (х, у) %3D…

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Q: Find an equation of the tangent line to the hyperbola y=3/x at the point (3,1)

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Q: transform into standard form of hyperbola x^2-y^2+6x-4y-4=0

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

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Q: 2- Write the equation of hyperbola that pass through point (12, 9) and have F1 (0, 0) and F2 (0, 4)V

A: Consider the given information. y−k2a2−x−h2b2=1 Since we have the given foci at F1(0,0) and F2(0,4).…

Q: Find the standard form equation for a hyperbola with vertices at (0,20) and (0,-20) and asymptote…

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Q: Find the standard form equation for a hyperbola with vertices at (6, 0) and (– 6, 0) and asymptote 1…

A: Find the equation of the hyperbola

Q: Find the equation of the conic section indicated. Parabola with vertex (4, −1), directrix x = 15

A: Vertex is 4, -1 and directrix is x=15. Now vertex is, h, k=4, -1⇒h=4  &  k=-1 & Directrix…

Q: Find the orthogonal trajectories for the family of ellipses with centers at the origin and…

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

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

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Q: 2 Find the transformed equation of the hyperbola xy = 4 when rotated 45. (x')² - (y')² = 8…

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Q: Find the minimum distance from the point (4,2) to the parabola y2 = 8x.

A: We have to find the minimum distance from the point (4,2) to the parabola y2=8x.

Q: Derive the orthogonal trajectories of the family of hyperbolas ??=?.

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

A: Introduction: When a multivariable function is to be extremized under some constraints, we use the…

Q: Which is the equation of a hyperbola with directrices at x = ±2 and foci at (4, 0) and (−4, 0)?

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

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Q: Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (1, 0). %3D (х, у)…

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Q: Find an equation of the hyperbola that has foci at (-10,0) and (10,0) , and asymptotes y=3x and…

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Q: Show that the line b2xx1 - a2yy1 - a2b2 = 0 is tangent to the hyperbola b2x2 - a2y2 - a2b2 = 0 at…

A: Find dy/dx.Then find dy/dx at the point (x1,y1) by plugging x=x1 and y=y1

Q: Find an equation of the tangent line to the hyperbola defined by 5x^(2)+4xy−2y^(2)−4x=19 at the…

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Q: If tangent lines to the hyperbola 9x2 − y2 = 36 intersect the y-axis at the point (0, 6), find the…

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Q: Find the minimum distance between the point (5,1) and the parabola y=-x2 ?.

A: Find the minimum distance between the point (5, 1) and the parabola y = -x2?

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

Q: What point on the parabola y = 3- x² is closest to the point (3,3)? The point on the parabola y = 3…

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Q: The semi-hyperbola H(X)=(sqrt(x^2-1)) is continous at which x interval?

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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: Find the points on the ellipse 2x +y 1 where f(x,y)= xy has its extreme values. %3D

A: Solution:- Here we have to find the extreme value of  f(x,y)=xy subject to constraint…

Q: Write the equation for the hyperbola with foci (1,-s), (2.-s) and conjugate axis of length 6. (x-…

A: Please refer the attached image for complete solution.

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: What point on the parabola y = 1-x is closest to the point (1,1)? The point on the parabola y = 1-x2…

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Q: Find the equation of the conic of major axis on the x-axis, the center at (0,0) passing through (2,…

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Q: Find the standard form equation for a hyperbola with vertices at (8, 0) and ( – 8, 0) and asymptote…

A: The standard form of the equation of a hyperbola with center (0,0) and transverse axis on the x-axis…

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

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Q: Determine the equation of the normal line to the hyperbola x^2 - 4y^2 = 9 at (5,2)

A: We have to find equation of normal

Q: Find the standard form equation for a hyperbola with vertices at (8, 0) and (– 8, 0) and asymptote 3…

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Q: Find the orthogonal trajectories of family of hyperbola with center at the original and the length…

A: The solution are next step

Q: Find the standard form equation for a hyperbola with vertices at (12,0)(12,0) and (−12,0)(-12,0) and…

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Q: Find the equation of the tangent plane to the hyperboloid in 2 sheets x2 - y2 - z2 = 4 at the point…

A: We have to find the equation of the tangent plane to the hyperboloid x2-y2-z2=4 at the point 3,2,4.

Q: Suppose the axis of a parabola is parallel to the yy-axis and passing through the points (0,3),…

A: Given that, the axis of a parabola is parallel to the y-axis. Let the Vertex of the parabola (h, k)…

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

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