Find a Cartesian equation for theplane tangent to the hyperboloid x2 + y2 - z2 = 25 at the point(x0, y0, 0), where x02 + y02 = 25.

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

A:

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

A:

Q: The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. Use Lagrange…

A: Note that here we have to extremize x2+y2+z2 , whch is eqivalently ,to extrimize x2+y2+z2.

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: 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 standard equation of the sphere with center (−3, 2, 4) that is tangent to the plane given…

A: Radius (r) will be the distance from the center to the tangent plane. That is the distance between…

Q: Determine the points on the surface y2+z2−x=8 that are closer to the origin.

A: Consider the given surface. y2+z2−x=8z2=8−y2+xf(x,y)=8−y2+x

Q: Find the standard equation of the sphere with the given characteristi Center: (-1, -9, 7) Radius: 9…

A:

Q: The plane 15x + 20y + 40z = 195 intersects the cone z = x² + y² in an ellipse. The sum of the…

A:

Q: Find and equatin for the parabolid z = x^2+y^2 in spherical coordinates

A: Given query is to find equation of paraboloid in spheo coordinates.

Q: Find the points on the surface x² −yz = 5 that are closest to the origin.

A: Let the point P be (x,y,z). The distance between the point P and origin is given by the formula…

Q: Find an equation of the sphere with center (2, 1,−3) that is tangent to the plane x −3y + 2z = 4.

A:

Q: Match the description of the conic with its standard equation. Hyperbola with vertical transverse…

A: We have to identify the standard equation of a hyperbola with vertical transverse axis. Let h,k be…

Q: 2. Find the equation of the plane tangent to the elliptic paraboloid z = point (1, 1,3). 2.a2 +y, at…

A: To find out the equation of the plane tangent to the elliptic paraboloid.

Q: Identify a generating curve on the xz-plane for the surface of revolution with equation x? + y? +z?…

A:

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

A:

Q: What is the highest point on the ellipse that is the intersection of the plane x + y + 2z = 2 and…

A: Given  the intersection of the plane x+y+2z=2 and the paraboloid z=x2+y2

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

A:

Q: Find the equation of the tangent plane to the paraboloid z = 2x2 +y? at the point (1,2,6). Select…

A:

Q: Consider the curve in the xy plane defined by the equation 4y? – 22 – 8y – 6x = 21 Show that this…

A:

Q: Find the orthogonal trajectories of the family of hyperbolas xy = c

A:

Q: What is the highest point on the ellipse that is the intersection of the plane z+y+ 2z=2 and the…

A:

Q: Sketch the xy-trace of the sphere whose equation is (x−3)2 +(y−2)2 +(z+4)2 =52.

A: We can find the xy trace by setting z = 0 in the original equation.

Q: Find the spherical equation for the hyperboloid of two sheets x² – y² – 2² = 1.

A: Given information :  Equation of hyperboloid of two sheets x2-y2-z2 = 1

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

A:

Q: (b) Find the equation of the tangent plane to the hyperboloid r2 + 3y? – 322 = 1 at the point (1,…

A: We have to find the equation of the tangent plane to the hyperboloid x² + 3y² − 3z² = 1 at the point…

Q: Find the equation of spheres passing through the circle x+y+z'-6x-2z+5 =0, y = 0 and touching the…

A:

Q: Find the point on the ellipsoid x2 + y2/4 + z2/9 = 1 for which x + y + z is largest.

A:

Q: What is the highest point on the ellipse that is the intersection of the plane z+y+ 2z = 2 and the…

A:

Q: Prove that the product of the perpendicular distances F1R1 and F2R2 from the foci to a tangent line…

A:

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: Given the curve of intersection of the x² + 4y² -z = 0 which is a paraboloid and the plane 2x - z =…

A: Solution:-

Q: Find the center C and the radius a for the spheres 3x2 + 3y2 + 3z2 + 2y - 2z = 9

A: Given: The equation of sphere as 3x2+3y2+3z2+2y-2z=9, To find: The center C and radius a for the…

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: What is the highest point on the ellipse that is the intersection of the plane z +y+ 2z = 2 and the…

A: I am going to solve the given problem by using the Lagrange's Multiplier method to get the highest…

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

A:

Q: Find the equation of the surface of revolution generated by rotating the parabola y = z^2 around the…

A: A surface of revolution generated by rotating a curve described by y=f(z) around z-axis is given as…

Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y2 + Z?…

A: Solution-

Q: Find an equation in spherical coordinates whose graph is the parapoloid Z=(X^2)+(Y^2)

A:

Q: determine a and b as to make the cylinder y^2=4ax orthogonal to the ellipsoid at point (1,2,1)

A: Given equation of the cylinder is  y2=4ax, say φ1=y2-4ax=0 and the general equation of the ellipsoid…

Q: Find symmetric equations for the tangent line to the curve of intersection of the paraboloid zx +y…

A: Given  The equation of Paraboloid Z=x2+y2 The equation of Ellipsoid 2x2+y2+z2=76

Q: Find an equation for the tangent plane to the hyperboloid x2+y2−z2=1 at the point (3,1,3).

A:

Q: Sketch the xy-trace of the sphere whose equation is (x+3)2 +(y−1)2 +(z−3)2 =18.

A:

Q: Find the y coordinate of the center of curvature of the parabola at (2,2). 7. -7 -6 6.

A:

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

A: Vertices of parabolas = (0,0), Foci on the y-axis.

Q: The tangent plane to the elliptic paraboloid z = -2x - 7y? at the point (-3, -4) is

A: Consider the provided question, The equation of the tangent plane to the elliptic paraboloid at the…

Q: Find a vector parametric equation for the ellipse that lies on the plane z (x + 2 - cylinder x + y =…

A: Dear student. You have posted many parts, according to the policy we will answering the first part.…

Q: Try to sketch by hand the curve of intersection of the parabolic cylinder y = x2 and the top half of…

A: Given that the curve of intersection of the parabolic cylindery=x2 and the top half of the ellipsoid…

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

A: Make equation of parabola