4 du + 3, du -o is dassified as Jhe P.O E dx² © Hyperbotic Elliptic Parabolic there of

Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 1) and directrix…

A: Given that Focus of parabola is F0, 1. Directrix is y=-1. We have to prove that y=14x2 is the…

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: Let S be the quadric with equation 36x² – 4y² – 9z2 – 36x = 0 • Classify the graph of S…

A: Given, S is the quadric with the equation                                36x2-4y2-9z2-36x=0

Q: The surface z -- =1is a hyperboloid of two sheets. Select one: OTrue OFalse

A:

Q: For hyperbola represented by 16z - 3y? – 32x + 12y – 44 = 0, which of the following is false. O…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Let P(x1, yı) be a point on the parabola y² = 4px with focus F(p, 0). Let a be the angle between the…

A:

Q: How many tangent planes to the hyperboloid r-y?-2 1 are parallel to the plane z= r +y? %3D

A:

Q: Find the equation for a hyperbola centered at (0, 0), with foci at (0, - V 52 -6) and (0, 6). y? x2…

A: Here we have to find the equation of hyperbola having a center (0,0) with foci at 0,-52 and 0,52 and…

Q: Which of the following is not a parametrization of the parabola y = r² ? Oz= Vt, y=t Oz-t, y-t Oz- ,…

A: We will check which parametrisation is correct.

Q: Which of the following conics has an eccentricity greater than 1? * 9x² + 16y² 36x +96y +36 = 0…

A: The eccentricities of conic sections are as follows. For circle e=0 For parabola e=1 For ellipse…

Q: A conic section is said to be circle if the eccentricity e = 1. Select one: O True O False

A: The eccentricity of a conic section is a non-negative real number that uniquely characterizes its…

Q: Find a rational point on the plane conic 2x2+y? = 6 other than the points (+1,±2). Show all your…

A:

Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 2) and directrix…

A: Given:            Focus of parabola is : F(0,2)Directrix is:​y=−2.

Q: Which of the following are parametric equations for the ellipse given by 9 apply. + y² = 1? Choose…

A:

Q: Which of the following is the equation of a sphere with radius r = (-1,0,-2)? Select one: O None of…

A: This question is related to equation of sphere, we will solve it using given information.

Q: and the plane - 3 X + Z Intersect along a line. Find Parametnic desenetion of this la

A:

Q: FINO THE OLUME FORMED BY REVOCVING THE HYPERBOLA xy - from to X=4 about the y- uxis

A: Here the curve is xy=6 and x changes from 2 to 4. we have to find the volume of the given curve

Q: Using the property of Re z and Im z to show that the hyperbola x2 - y2 = 1 can be written as: z² + (…

A:

Q: 14. The folium of Descartes can be parametrized by 31 1+' 3r y = a. Find the equation of the folium.

A:

Q: 103. Show that the parametrization of the ellipse by the angle 0 is ab cos 0 X = a² sin² e + b² cos²…

A: From given data,

Q: state whether the given equation defines an elliptic paraboloid, a hyperbolic paraboloid, or an…

A: Rearrange the equation, 3x2-7y2=z by dividing both sides by 21 and obtain x27-y23=z21. The general…

Q: Find parametric equations for the complete parabola x = y2. Answersare not unique.

A:

Q: find a parametrization for the curve. the upper half of the parabola  x-9=y^2

A: The given curve is x-9 = y2  ...(a) Putting y = t in (a) then x = 9+ y2…

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: 10. All hyperbolas center at the origin.

A: we know the equation of hyperbolas center at origin is…

Q: Identify the surface 2x² + 4y? – 1=0. A. An elliptic cylinder. B.Ahyperbolic cylinder. OC. None of…

A: We will solve the problem

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

A:

Q: Q.2. Show that the area of the ellipse =1 is z ab. ab

A:

Q: The equatione of aoymptoteo ofthe hyperbola 9 (y-9)2-4(x-7)2= 36 are Select one: O 2(y-9)=+3 (x-7) O…

A:

Q: Name the type of conic section defined by the following equation and give a parametrization of it:…

A: We know general equation of circle is given by  center at (a, b) of radius r is given by (x-a) ^2…

Q: State whether the equation 3x? – 3y² – 5z² = 1 defines | an elliptic cone. an elliptic paraboloid.…

A: As per our guideline i am supposed to answer only one question from these two images which contain…

Q: Prove that evolute of the ellipsé x2 y? = 1 a? b2 is (ax)2/3 +(by)2/3 = (a² – b²)²/3. %3D

A: Given equation of the ellipse be x2/a2 + y2/b2 = 1 Write the equation of the ellipse in parametric…

Q: 3) Find the family of curve that intersects the family of hyperbolas y = 2r+b at an angle arctan(1)…

A: Given the equation of family of hyperbolas is y2=2x2+b

Q: How did he get the value inside the circle Given, 2 = xay2 and x-y+22=2 >2 = 1- - ellipse fox n is…

A:

Q: Find the parametric and symmetric equation for the satisfying the given condition. 1. Through the…

A:

Q: .2 The surface z? = 1 is a 25 - - 36 hyperboloid of one sheet. Select one: OTrue OFalse

A:

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: Evaluate (2y + 1) dS, where S is the part of the plane 2x+2y+z=6 that lies in the first octant.

A:

Q: For the quadric surface, - + z = = 1, setting the value of z = 1will give you which conic section? 4…

A: The given quadric surface is x24-y29+z=1  To find when z=1which conic section represents the…

Q: Using the property of Re z and Im z to show that the hyperbola x2 - y? = 1 can be written as: z +…

A:

Q: to prove thát thế answers 20. Parabolas with vertex and focus on the x-axis. 21. Parabolas with axis…

A: We have to Find the Differential Equation of the Family of Parabolas with vertex and focus on the…

Q: Using the property of Re z and Im z to show that the hyperbola x2- y2 = 1 can be written as: z? +…

A: We know that x=Re(z)=z+z2 and y=Im(z)=z-z2i. We are given the equation of hyperbola x2-y2=1.

Q: Using the property of Re z and Im z to show that the hyperbola x2 – y? = 1 can be written as: z² +…

A:

Q: Prove that using the only the form of the given equation (no graphing) that it is a paraboloid.…

A: We need to prove that the the equation: x2+z2-y4=1 is a paraboloid.

Q: 4. Classify the type of the equation as elliptic, parabolic or hyperbolic. Uxx xuy+xu 0 =

A: The given problem is to classify the given partial differential equation as elliptic, parabolic or…

Q: The length of the latus rectum of a hyperbo is equal to 18 and the distance between the foci is 12.…

A: Here, given that the conjugate axis is parallel to the y-axis. So, the equation of the hyperbola is…

Q: 2uzz – 6uzy – 8uyy и, (0, у) — 4у and u, (0, y) — eV. Is this equation elliptic, parabolic or…

A:

Q: 32. Which of the following is the trace of the surface in the plane y=3? Hyperbola Ellipse Parabola

A: Consider the given surface as 9x2+z2-3y=0

Q: Identify the surfaces of equations in the Cartesian form. Show your complete solutions. (a) 2² = 4 +…

A:

Q: A hyperbola in standard position has equation 9x 2 − 15y 2 − 16 = 0. Write down a parametrisation…

A: We will first parametize the curve