C'enter of the hyperbola x? + 4y? + 6xy + 8x 2y + 7 = 0 is - A. (1, 1) В. (0, 2) С. (2,0) D. None of these B.

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: The part of the hyperboloid 4x 2 - 4y2 - z2 =4 that lies in front of the yz-plane

A:

Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

A:

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: 4.) Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

A:

Q: What is the equation of an ellipse with its center at (-2, 1), a major axis 16 units long, and…

A: Write equation of parabola

Q: Write the equation for the hyperbola with foci (1,-5), (9.-5) and conjugate axis of length 6. (x-…

A:

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

A:

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

A:

Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

A:

Q: 91 a) Find an equation of the sphere with center (1,-3,-5) and tangent to xz-plane.

A:

Q: 2. What is the equation of a horizontal hyperbola with (x-4)² 81 (y + 3)² 81 (x-4)² 25 (x-3)² 25 (y…

A: Given problem:- What is the equation of a horizontal hyperbola with a center at (4,-3), a transverse…

Q: Determine the length of the latus rectum of the following conic section: 16z + 9y? - 64.x- 54y+1 0 O…

A: 16x2+9y2-64x-54y+1=016x2-64x+9y2-54y=-116(x2-4x)+9(y2-6y)=-116(x2-4x+4)+9(y2-6y+9)=-1+64+8116(x-2)2+…

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

A:

Q: What kind of conic section (or pair of straight lines) is given by the quadratic form Q(x1, x2) = x…

A:

Q: z= 2e'+i

A:

Q: Show that the “conic section” with equation x2 − 4x + y2 + 5 = 0has no points.

A: Equations for conic sections are obtained as the locus of points following one or a set of…

Q: 5. plot x?-y?=z (Elliptic paraboloid) in 3D.

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: Show that the tangent line at a point P = (x0, y0) on the hyperbola(x/a)2−(y/b)2= 1 has equation Ax…

A: Given equation of hyperbola  x2a2-y2b2=1 and given point is P=xo,yo. Since hyperbola is passing…

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: 2.5 What is the distance between two parallel hyperplanes {r E R" | a"x = b1} and {r E R" | a"x =…

A:

Q: 3. Find the area of the surface cut from the nose of the paraboloid x = 1-y²-z2 by the yz-plane. Do…

A: Surface area in yz-plane

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

A:

Q: Find the point on the sphere x2 + y2 + z2 = 4 farthest from the point (1, -1, 1).

A:

Q: Find the standard equation of the sphere with center (-6, 2, 7) that is tangent to the plane given…

A:

Q: 2.5 What is the distance between two parallel hyperplanes {x E R" | a"x = b} and {x E R" | a"x =…

A:

Q: The center of the hyperbola 25x² – y + 150x – 6y+191=0 is %3D A (-3,-3) B (3,-3) (3,3) D (-3,3)

A:

Q: Determine the equation of the normal line to the hyperbola x - 4y- = 9 at (5, 2). 8x + 5y – 50 = 0…

A: Given equation of hyperbola is  x2-4y2=9          ...(1) We have to find the equation of the normal…

Q: Find an equation of the tangent line to the hyperbola defined by (5x^2)+(4xy)−(2y^2)−4x=195 at the…

A:

Q: What are the asymptotes of the hyperbola 9æ? – 4y? – 18æ + 24y + 9 = 0 O (y – 3) = +(x – 1) ㅇ (y-3)…

A:

Q: Find the points on the hyperboloid 9x^2  - 45y^2 + 5z^2 = 45 where the tangent plane is parallel to…

A:

Q: he cylinder x² + y² = 2y and the plane

A: Shift cylinder at origine as centre

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

A:

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

A:

Q: Determine the type of conics for each equation using the discriminant. 20. 5x2 + 2x + 3y - 5 = 0 21.…

A:

Q: Find an equation for the plane tangent to the surface z = 2x2 - 7y at the point (3,-1,5)

A: Given surface z=2x2-7y and the point 3,-1,5. The main objective is to find an equation for the plane…

Q: 4x? + у? - 327 25 3z2 = 25

A:

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

A:

Q: Find the point on the sphere  x2+y2+z2=7056 that is farthest from the point (5,−15,−2)

A: The given question has been solved in detail

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

A:

Q: 1. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch es. %3D

A: Topic = Geometry

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: - Show that the distance r from the origin O to the point P(Coshu,Sinhu) - on the hyperbola x-y 1 is…

A:

Q: The point of the sphere with equation X x²-2x +y²-4y +z²-6z+10=0 nearest to the xz-plane is 0.

A:

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: what is the equation of the geodesic in the hyperbdic upper half-plane that joins -1+i with Iti

A:

Q: Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

A: This is a problem of geometry. We will calculate slope of x, y and z at given point and general…