for the given audratic equation determine, i- which way the parabolla opens ii- the cordinate of the vertex iii- the roots of the functions 1- y=x2-3x+2 2- y=2x2-3x+1

Q: For Exercise, find an equation of the form  y = ax2 + bx + c that defines the parabola through the…

A: Consider the given equation of parabola:

Q: For the hyperbolic PDE u, +bu, =0 a) Find the finite difference equation, using forward for u, and…

A: Given: The given hyperbolic PDE  ux + buy = 0 a) To find the finite difference equation, by using…

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

A: According to the given information, it is required to find the maximum and minimum value of the…

Q: Find the maximum and minimum values of the function f (x,y) = 2x² – y² on the ellipse p² + 2 (y –…

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Q: Find the angle at which the parabola y=x2−14 intersects the positive x−axis.

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

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Q: The equation of the parabola culminating at P (1,4) and through (3,0) is f(x)= ax^2+bx+c, so the…

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Q: Find the equation of the directrix and the length of the latus rectum of the given parabola.…

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Q: The surface of a mountain is modeled by the equation h(x, y) = 7000 - 0.001x2 - 0.004y2. A mountain…

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Q: Cоmрute (x + y) dz, where is the portion of the parabola C y = 4 – x2 from -2 to 1+3i.

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Q: 13. The parabola y = x2 + x + 1 opens: A. To the right %3D B. To the left C. Upward D. Downwarč

A: y=x2+x+1 here parabola is in the form of y=ax2+bx+c which means it can be open up or down…

Q: Show that line d:3x-4y-5=0 is tangent to hyperbola H:x2-4y2=5 and find the point of contact of the…

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Q: Below the paraboloid z = 18 – 2x² – 2y² and above the xy-plane -

A: The region D lies below the paraboloids z=18-2x2-2y2 and above the xy-plane.

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

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Q: A point moves on the parabola 10y = 5x² + 3 in such a way that when x = 6, the abscissa is…

A: Given: A point moves on the parabola 10y=5x2+3, when x=6 the abscissa is increasing at the rate of 2…

Q: The graph of the curve described by the paramnetric equations x = 3t – 4, y = 6t + 2 is a straight…

A: Consider the curve  x=3t-4,y=6t+2

Q: Find b and c, given that the parabola y = x2 + bx + c passes through (0, 5) and (3, 23).

A: (0,5) means when x=0 then y=5. similarly, (3,23) means when x=3 , then y=23.

Q: Show that the number 4p is the width of the parabola x2 = 4py (p>0) at the focus by showing that…

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Q: 8. Calculate fo F • dr, where F(x, y) = y² i + (6x + 6y)j, and C is the portion of the parabola 2y²…

A: Given curve is 2y2-x=1 and points are (1,-1) to (7,2)

Q: Let F(r, y) = (x + 1)7, and let C be the portion of the parabola y = x² that starts at (0,0) and…

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Q: on the hyperbola xy = 1. %3D Which of the followings is TRUE for f(x, y) = x² + y? %3D Litfen birini…

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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: An equation for the level surface passing through the point (2,0, - 1) is z =

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Q: Consider the hyperbolic PDE shown below = 4- at? For a value of At=0.1, what are the values of Ax…

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Q: 1. For the parabola equation: (y-2) = -3(x+4)^2 + 7, in which direction does the parabola open? *

A: We have to find the direction in which the given parabola opens.

Q: 2. Write the general equation of the parabola with directrix at x FG,-1), and v (. -1). 2

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

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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: Find the midpoint m of z1 = (8+5i) and Z2 = (12 + 3i). Express your answer in rectangular form. m =

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Q: 4. Consider the equation of the hyperbola given by x2 + 2xy – y² = 7. Find an equation of the…

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Q: Fid the equation of the tanget to the parabola  x2 - 22x + 24y +169 = 0 at  the point whose focus…

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Q: drawn from the point A(2,10) on the parabola y = x^2 + bx + c Since the tangent is parallel to y =…

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Q: The value of y dæ – x dy where C is the portion of the parabola y = x² – 1 from (0, –1) to (-2, 3)…

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Q: - z²) – 2x + 30y = 0 da? What is the larger root from the indicial equation

A: Given differential equation, 1-x2d2ydx2-2xdydx+30y=0 Find the largest root from the indicial…

Q: For the parabola -2x 16y +4y2 + 13, for what value of y does r have a minimum?

A: This question is taken from the calculus in which we have to find the value of the y which makes the…

Q: Find an equation of the paranola in standard form: with the vertex at V (2,-4) and directrix y= -5

A: Find an equation of the parabola in standard form: with the vertex at V (2,-4) and directrix y= -5

Q: The parabola y = Px² + Qx + R_passes through the coordinate (1,1) and has b. Determine the values of…

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Q: A spotlight is made by placing a strong light bulb inside a reflective paraboloid formed by rotating…

A: Let's find how far from the vertex should the bulb be placed.

Q: The tangent and the normal to the parabola y²=20x at the point T(5,10) meet the x-axis at the points…

A: Details solution is given below:

Q: By means of Lagrange's formula, prove that 1 Yo = - 1 - [2 (y₁+y_₁). (Y3 - y₁) 2 -Y₁) - 2 (Y-₁-y-3)…

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Q: The area of the region to the left of the parabola x=2y^2, to the right of the y-axis, and between…

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Q: The indicial equation of (r – 1)?y" + (x³ – 1)y' + 2y = 0 at = 1 is :

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Q: Let f(x, y) = x? + 4y. Find the extreme values of f on the ellipse x? + 2y? = 1.

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Q: In the 3D coordinate system, for the quadric with euqation ax2 + y2 + 4z2+x + 6y − 4z = −a − 10…

A: The quadric with equation ax2 + y2 + 4z2+x + 6y − 4z = −a − 10 where a is a parameter. We need to…

Q: 1. Find the point on the parabola y = 3 – x² that is closest to the point (6, 0).

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Q: Find the diffrential equation of for each of the curves determined by the condition that at each…

A: length of subtangent =ydydx

Q: The line x=C where C70 intersects the cubic y= 2x3 + 3x²-9 a七 the point P and parabola y = 4x+ 4x +5…

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Q: I For the parabola -2x = 16y + 4y² + 13, for what value of y does x have a minimum? 3. If the

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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

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.