What kind of conic section is given by the quadratic form ? -11x,2 + 84x,x2 + 24x,2 = 156 Transform it to principle axis. Express x" = [x1 X2] in terms of the new coordinate vector y" = [y1 y2] %3D

Q: What is the image of the point (4, 5) after a rotation of 90° counterclockwise about the origin?

A: Given data: The given coordinate of x is x=4. The given coordinate of y is y=5. The given angle in…

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

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Q: Perform a rotation of axes to eliminate the xy-term, and sketch the graph of the conic.xy = 3

A: We need to rotate the axes by θ = π / 4 Hence,  x' = x cos(θ) + y sin(θ) = (x + y)/√2 y' = - x…

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: The scalar  equation of the plane passes through (-1, 3, -2), (-1, 2, -1) and (4, 1, -2) is:   a.…

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Q: 9. Find equation (in an Rectangular) for the conic that satisfies the given conditions: Parabola…

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Q: Write an orthogonal change of coordinates converting the equation of the conic 3x2+3y +3z+2ry+2rz…

A: Given equation , 3x² + 3y² + 3z² + 2xy + 2xz+2yz = 1

Q: What is the standard form of the conic defined by x + 2y² – 8y = 0?

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Q: 8. Find a parametric representation of the line through the point P(1,0,4) and perpendicular to the…

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Q: What specific (include direction/opening and vertex/center) conic section is 4x + y + 72x + 14y +…

A: topic- algebra

Q: Write the equation of a conic given by x2 – 9y2 + 2x- 54y-80=0 in standard form. (x+ 1)² (y+3)? 162…

A: The objective is to write the equation of conic in standard form.

Q: Here is the equation of a conic section such that the ordered pair (Vx, Vy) corresponds to its…

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Q: Q.8: ] find the parametrization of the upper half of the conic section 4x² +9y²-24x = 0; with x= -2

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Q: 20) Find the coordinàtes of the foci of the conic x² –10x –16y² – 64y – 55= 0

A: We write the given conic in standard form Then we compare it with the standard equation of a…

Q: Identify the conic with th e given equa­tion and give its equation in standard form…

A: Given, The equation is 6x2 - 4xy + 9y2 -20x -10y - 5 = 0.

Q: 18 Identify the center of the conic section whose equation is 5x 2 + 9y 2 - 80x + 54y + 221 = 0…

A: Solution is here

Q: Determine the type of conic: 16. 2x2-4xy + 8y2 +7 = 0 17. 2xy-x + y-3 = 0 %3D %3D

A: The general equation of conics is given as Ax2+Bxy+Cy2+Dx+Ey+F=0, where A,B,C,D,E and F are real…

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

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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: Identify the type of conic from the discriminant.* x²+2xy +y² + /2x-/2y-2=0, 6=45° ANSWER: BIlank 1…

A: Given problem Given that   General equation of the conic : Ax2+Bxy+Cy2+Dx+Ey+F =0 Discriminant is…

Q: The conic section whose equation is 3x 2 - y 2 - 27 = 0 has a latus rectum equal to 9 18 6

A: Given:  Conic section : 3x2-y2-27=0  To find latus rectum

Q: Find the orthogonal trajectories of the family of ellipses with centers at (0, 0) and two vertices…

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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: How do I find the focal points of this conic?  27x2+16y2+324x-96y+684=0

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Q: If P1 and P2 are two points on the conic whose angles θ1 and θ2 differ by 180° , show that the…

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

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Q: Standardize the conic whose equation is 7x2 + 4xy + 4y2 - 2x - 6y + 1 = 0.

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Q: Find an equivalent quadratic form by using a diagonal rotation, (by the principle axis theorem. I…

A: Given: Q=2x2+4y2+6yz-4z2=80

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: 1- Sketch the following conic sections: Aa-. y-4y+8- 4x2 -0 b- y2 -4y-4x2 = 8 c- 3(y- s)2 - 7(x +…

A: Since, you have asked multiple questions , we will solve the first question for you. Also, the first…

Q: Give a parametric representation for the cylinder x^2+z^2=121

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Q: Use a translation of axes to put the conic in standard position. Identify the graph, give its…

A: First, we write x and y terms together, so it becomes, x2 - 4x + y2 - 4y = -4 By using completing…

Q: 1- Sketch the following conic sections: 2-4y+8-4x2- b- y2 -4y-4x2 = 8 C- 3(y-s)2 -7(x+1)2 =1

A: As per our guideline we are allowed to do 1 question or 3 subparts at a time. Please post other…

Q: What is the image of the point (4, 0) after a rotation of 90 counterclockwise about the origin

A: Under rotation 90° counter clockwise about the origina point (x,y)→(-y,x)Hence (4,0)→(0,4)

Q: 9. How can you determine the type of conic section represented by an equation in general form?

A: How can you determine the type of conic section represented by an equation in general form ?

Q: O Reduce the equation x + 2ry +y +4 V2x - 4V2y = 0 to the standard form and hence %3D identify the…

A: The given equation is x2+2xy+y2+42x-42y=0

Q: Identify and sketch the conic defined by x2 - 2xy+ y² – x – y=0.

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Q: Find the eccentricities of each of the conics given below. (a)        y = 4x2 − 2019x + 83 (b)…

A: Given that: (a)        y = 4x2 − 2019x + 83 (b)      x2/42 + y2/62=1 (c).     x2/42 − y2/62=1

Q: 2. Identify the conic section given by y² + 2y = 4x² + 3 Find its vertex/vertices and focus/foci.

A: We rewrite the equation as: This is an equation of a hyperbola.

Q: (b) Show that the equation r² – 4x + 4y2 – 12 = 0 represents a conic section. Sketch the conic…

A: To show: The equation x2 – 4x + 4y2 – 12 = 0 represents a conic section.Proof:

Q: What are the intersections of the conic section formed by the points A(0,1),B(2,3),C(5,4),D(1,…

A: Below are graph and input view.

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

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Q: Use 0 = 30° to write -=1 in the x'y´ plane. The- conic. O 18(x)² +16/3x'y – 2()² – 88=0; ellipse…

A: Here we have to use θ=30° to write x24-y29=1 in the x' y' plane. and identify the conic.

Q: Use a translation of axes to put the conic in standard position. Identify the graph, give its…

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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 Identify the center of the conic section whose equation is x 2 +y 2 + 6x - 4y - 12 = 0. (-6, 4)…

A: The given equation is; x2+y2+6x-4y-12=0   As we know that; The general form of equation of the…

Q: Consider the conic below x² + 4xy+ 4y² – 2/5x + /5y = 0 and determine what is asked. Translation…

A: Here, the given equation is x2+4xy+4y2-25x+5y=0. Firstly, let's evaluate the angle of rotation, θ.…

Q: Identify the center of the conic section whose equation is 4x 2 - 25y 2 - 8x - 100y - 196 = 0. (-1,…

A: We can identify the center as below.

Q: Write the equation of a conic given by 8x² + 8y² – 16x + 48y+ 10 =0 in standard form. A (x- 1)² +…

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

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