(a) Classify, according to type (hyperbolic, elliptic, parabolic) the following equations: (i) 3Uxx +4Ury - 8Uyy = 0. (ii) Uxx-5Ury +6Uy – 7U, = 0. %3D %3D

Q: Which of the following equations is the equation of tangent to the parabola y2 = 2x + 8 at point…

A: The given equation of parabola is: y2=2x+8

Q: Determine the general equation of a parabola opening downwards whose vertex is at (3,-4) with a…

A:

Q: Find the parametric equations of the solutions to the following linear system x + 2y – 3z = 4 -2x –…

A: From the given system of equations, we can write the matrix as 12-3-2-4636-94-812 R2+2R1, R3-3R1…

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: equation of parabola:-

Q: The system of conics has two solutions. (z – 4) + (y+1)* = 9 (9+1) 1. +- 81 What are the solutions…

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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: Consider the parabola y = -x +4x + 9 and the line y=2x + 1. Solve for the x-coordinates at their…

A: x - coordinates of the point of intersection = ?

Q: In the xy-plane, a line that has the equation y = c for some constant c intersects a parabola at…

A: in the xy-plane a line that has the equation y=c for some constant c intersects a parabola at…

Q: (b) Find an equation for the parabola that has axis x = -1 and passes [3] through the points (4,5)…

A: Directrix is a line which together with a point called the focus defines the set of points that form…

Q: 3- The parabola y= ax'+bx+e, mean that the equation y ax' is . .........

A:

Q: What is the equation of the parabola containing the points (0, 5), (–1,9), and (2, 3)? O y = r-z+5 O…

A: The standard form of a parabola is y=ax2+bx+c. The required parabola passes through the 3 points are…

Q: If a person shoots a basketball overhand from a position 8 feet above the​ floor, then the path of…

A:

Q: Determine the point on the hyperbola −9x^2+7y^2=10 closest to the point (-9, 0). Give the x…

A: Here we have to find the point on the hyperbola -9x2+7y2=10 closest to the point (-9,0).

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: Here we have to find the equation of the parabola that has its vertex at the origin  and Directrix:…

Q: Find the equation of the parabola, y=ax^2 + bx + c, that passes through the points (1,4), (-1,0),…

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Q: Two stations that are 2 km apart receive a sound signal issued from a source located at point…

A: The distance between the point 0,-1 and the point P (x, y) is, d1=x2+y+12 The distance between the…

Q: find the equation of the parabola y = ax? + bx + c that passes through the points. (0, 3), (1, 4),…

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Q: Select a possible equation for a parabola with a vertex of (-1,3). Oy = (z + 1) (x – 3) | Oy = (z -…

A:

Q: What is the equation of the directrix of the parabola x2 + 2x+4y– 27=0? A y=8 B y=0 (© y= -2 D y=6

A: Solution ) x2 + 2x + 4y - 27 = 0 Add 1 and subtract 1 in equation  x2 + 2x +1  - 1  + 4y - 27 = 0…

Q: -x* + 4xy – 2y² + 1. Find the maximum value of the function f(, y) = 6 – 4x2 – y² subject to the…

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Q: II. Find the standard form of equation of hyperbola and determine the center, transverse axis, a and…

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Q: Solve the system -2 2 dx dt -4 2 with x(0) %3D -2 Give your solution in real form. %3D 22 = %3D An…

A: The given problem is to solve the matrix differential equation with given initial condition.

Q: What is the axis of symmetry of the parabola y=1/4x^2−14x+28?   A. y=28 B. x=7 C. x= -14 D. x=28

A: Given y=14x2-14x+28

Q: What is the equation of a parabola that intersects the x-axis at points (-1, 0) and (3, 0)?   A. y…

A: Given that: A parabola intersects x-axis at (-1, 0) and (3, 0)

Q: The system of conics has two solutions. (z – 4)° + (y + 1)* – 9 (v+1) 6. +. 81 -1 What are the…

A:

Q: -10 10 -6 y? = 1. 62 Identify a and b for the hyperbola with equation - a = b = 6 3.

A: Given, The graph of the  hyperbola  The equation of the hyperbola is x2a2-y2b2=1  We have to find…

Q: 18. The equation of the parabola is y2 + 24x + 144 0. Solve the following. Standard form of the…

A: According to the guidelines in case of Multipart questions we are only allowed to do first four…

Q: Cartesian

A:

Q: Find the maximum and minimum values of the function f(x, y) = xy on the ellipse given by the…

A: We have the given function is f(x,y)=xy    ..... (1)   The equation of ellipse  x2+y24=1 Let…

Q: Find the equation of the plane perpendicular to the y-axis and passing through the point (3,2,-2)

A:

Q: Which of the following equations of parabolas has its vertex at (1, 2)? O y= 12 + 2x + 3 O y= r² +…

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Q: y -1 Q2) L, =Xx2 = -1 - 2 Fand equation of plane Canternng them

A:

Q: What is the equation of the parabola in general form given its vertex at (-1,-5) and focus at…

A:

Q: 2. Does the equation x² + y² + z²-3x - y + 3z = 0 represent a sphere? If so, find the center and the…

A:

Q: Find the equation of a hyperbola whose vertices are (+2,0) and whose foci are (+5,0). x2 A) 4 = 1 21…

A:

Q: 1. Determine the foci, vertex, and directrix of the parabola with the given equation. (a) x2 = 10y…

A: Dear learner, as per our guidelines , g can solve only 3 subparts of one questionat once. Further…

Q: x ds, where C is the portion of the parabola from (0,0) to (1, 1), followed by the line segment from…

A:

Q: the center-radius of the equationn 9x²-18 x+ 9+9y? + 12y=12 be obtained by adding both sides of the…

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Q: 1. If y varies indirectly as a, and y = 3 when a = 4, what is y when a = 6? %3D y = 2 y = 1 y = 4 y…

A:

Q: Q11

A: Just join the centres of two parabolas and draw a line joining them, it is called transverse axis.…

Q: IV. Name the conic section, based on the equation. x²+y +333x+444y+777 =0 3x + 2y? +12x- 4y+2=0…

A:

Q: 2. Which of the equations below also represents the parabola y=-3x² 18x + 16? Oy=3(x+3)² +65…

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Q: A pool is built in the shape of an ellipse, centered at the origin. The maximum vertical length is…

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Q: Find all the values of b such that the parabola y=(1)/(8)x^(2)-bx+(9)/(2) will have a directrix…

A: the given equation of the parabola is y=18x2-bx+92. we have to find all the values of b so that the…

Q: Find the equation of the Hyperbola whose Foci are at (2,1) and ( 10,1),and the length of its…

A: Given: Foci ≡ 2,1 and 10,1, Length of the Transverse axis = 4

Q: Given the following general equations, which one represents a hyperbola? O 2x2 + 4x – y² + 4y – 4 =…

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Q: 3. Write the equation into the standard form of the equation of the hyperbola: x² – 4xy + y² + 8x +…

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Q: Find the equation of the line tangent to (a) The parabola z = 2x² - 3y², y = 1 at the point (-2,1,5)…

A: Given: we have to find equation of tangent lines   equation of tangent line : y-y1=m(x-x1)