5. Sketch the parabolas showing the intercept and the maximum/minimum points. a) y = 2x – 4x +7 b) x' - 4x + y +14 = 0 c) y = 2x? – 3 d) y = -1-x?

Q: Find the equation in rectangular coordinates of the quadric surfaceconsisting of the two cones φ =…

A: The relation between spherical and rectangular coordinates in polar form is given by the following…

Q: Show that the parabola y = ax2, a ≠ 0, has its largest curvature at its vertex and has no minimum…

A: Using the relation,

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A: Let 2x and 2y be the length and width of rectangle with sides parallel to the coordinate axes, that…

Q: Find the distance from the point (−3,0,2) to the plane - 3x + y + 5z = 0

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Q: B) Use Lagrange multipliers to find the points on the ellipse 2x2+y? = 1, where f (r, y) = ry has…

A:

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (-2, -2, 0)

A:

Q: Find the locus of the foot of the perpendicular from the center of the ellipse x²/a²+y²/b² = 1 on…

A: Let end points of chord be P(acosθ,bsinθ) and Q(acosθ-π2,bsinθ-π2)that is P(acosθ,bsinθ) and…

Q: A rod of given length (a+b) unit moves so that its ends are always on coordinates. Prove that the…

A: The two ends of the rod is always on coordinate axes. Let's take one end P of the rod is always on X…

Q: What is the shortest distance from the surface xy + 15x + z2 = 204 to the origin? distance =

A:

Q: ` What is the shortest distance from the surface xy + 9x + z² = 76 to the origin? distance =

A: z2+9x+xy=76z2=76-9x-xy   ---- Eq 1Let P(x,y,z) be a point on the given surface. We know that…

Q: On a separate piece of paper, sketch the graph of the parabola y = x² + 9. On the same graph, plot…

A: Sketch the figure.

Q: Given a sphere in center-radius form, how will you get an equation tangent to only one of the…

A:

Q: Find formulas for the distances between (0, 0) and (a, a2 ), a > 0, along the line between these…

A: Derivative of a function is determined as the change of variable with respect to change in another…

Q: Determine the area of the largest circle that can be enclosed by the two hyperbolae, xy= 1 and xy =…

A: Solution is here

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

A:

Q: the sum of the distances from (x,y) to (-1,0) and from (x,y) to (1,0) is 4. show x and y is related…

A: Distance from (x,y) to (-1,0) is:  Distance from (x,y) to (1,0) is:

Q: A hyperbola is the set of points in a plane, the difference of whose distances from two fixed points…

A: Given : A hyperbola is the set of points in a plane the difference of whose distances from two fixed…

Q: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

A: Consider the given parabola y2=4ax Suppose Ax1 , y1  and  Bx2 , y2 be the ends of the focal chord of…

Q: What is the minimum vertical distance between the parabolas y = x² + x en y = x – x²?

A:

Q: On a separate piece of paper, sketch the graph of the parabola y = x + 3. On the same graph, plot…

A: Given: Equation of parabola, y=x2+3

Q: Calculate the curvature of the ellipse x2a2+y2b2=1 at its vertices.

A:

Q: A stationary artist intends to make rectangular cut-outs from the elliptical cardboard that he has.…

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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: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

A:

Q: Find the point on the parabola y = x^2 closest to the point (−3, 0)? and give the minimal distance?

A:

Q: Find the lines tangent to the ellipse x2/4 + y2/9=1 that contain the point (4, 0).

A: We at first consider the equation of tangent  to x2/4 + y2 /9=1 with slope m. Then we find the value…

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: Compute the length of the latus rectum of the ellipse x2 + 2y2 +4x+ 4y +4=0

A: Given:    x2 + 2y2 +4x+ 4y +4=0

Q: Let S be the quadric with equation 36x² –4y² –9z² – 36x = 0. Sketch a graph of the surface with…

A:

Q: The length of the major axis of the cllipse with center (-4, 1), minor axis parallel to the y-axis…

A: Equation of ellipse with center (-4,1) is given by

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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: Is the set of all points in a plane, the difference of whose distances from two fixed points (the…

A: For the given statement

Q: Find the distance between the pointx1 =−1, y1 =1, z1 =3 and the point x2 =1, y2 =1, z2 =1.

A: The first point is (-1,1,3) and the second point is (1,1,1) We will use the distance formula:

Q: What is the shortest distance from the surface xy + 6x + z² = 48 to the origin? distance =|

A:

Q: . (a) Show that as (x, y)→ (0, 0) along any straight line y = mx, or along any parabola y = kx², the…

A: Given : f(x) = x³y/(2x^6+y²)  To find : To prove that limit exist along parabola

Q: what is the minimum vertical distance between parabolas y = x2 + 4 and y = x -x2

A: Given: The equations of two parabolas are: y1=x2+4 y2=x-x2 We have to find the minimum vertical…

Q: Find the equation of the surface of revolution generated by rotating the hyperbola x^2 - y ^2=1 ,…

A: \ Revolution of the hyperbola about its transverse axis generates a surface of two sheets, two…

Q: Find the minimum distance from the parabola: x - y2 = 0 to the point (0,3).

A: x - y2 = 0 x = y2  Let us take a point (x,y)=(y2, y) on the parabola

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

A:

Q: A parabola has an equation of y²=2x, compute the radius of curvature at point (2, 2)

A:

Q: It has been shown that when like particles with a common charge are hurled at each other, they…

A: Let's find.

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: Find the area of the surfaces The surface cut from the “nose” of the paraboloid x = 1 - y2 - z2 by…

A: The surface cut from the '' nose '' of the paraboloid x=1-y2-z2 by the yz plane .…

Q: The length of the latus rectum of the ellipse defined by 25x2 +9y2 - 300x – 144 y + 1251 = 0 is 3.0…

A:

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

A: Let,f(x)=x2+y2-z=0and g(x)=x+2y+2z=2Our constraint is,∇f(x)=λ∇g(x)

Q: Sana wants to recycle some elliptic cardboard into rectangular name plates. The minor and major axes…

A: Given problem is : Sana wants to recycle some elliptic cardboard into rectangular name plates. The…

Q: What are the coordinates of the highest point where the circular cylinder intersects the Elliptical…

A: We will use lagranges multiplier theorem to find heighest point

Q: The maximum vertical distance between the parabola y = 3-z and the line y = 3x+2 on the interval…

A: