Graph the following by identifying center, foci, vertices, directrix, and/or asymptotes. (а) у? — 4у — 4х —D 0 (x – 3)2 (b) (y – 1)? :1 16 25 (c) 9х2 — у? — 36х — 6у + 18 %3D0

Q: Find the equation of the Hyperbola whose Foci are at (6,4) and ( 30,4),and the length of its…

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Q: 1. Determine the orthogonal trajectories of the family of ellipses 16x² + 121y? = c. Sketch some of…

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Q: Find the equation of the parabola with vertex at the origin and satisfies the condition: Focus…

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Q: What is the standard form of the parabola, y + 2x + 10y + 9 = 0, given in conic form?

A: Do some rearrangement in the equation of given conic to convert it in standard form of equation

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: Find the asymptotes of the cissoid of Diocles defined by the equationy2(2a−x)=x3,a>0.

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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: What is the equation of a parabola in standard form with vertex V(3, – 3) and focus F(3, 2)? A (x-…

A: NOTE: Refresh your page if you can't see any equations. . the vertex is at  and the focus is at

Q: The parabola y=x^2+13 has it's focus at the point (b,c) where  b= c=

A: The given equation of the parabola is, y = x2+13. Also the parabola has its focus at (b, c).Consider…

Q: Consider the graph of  y = ax2 + bx + c, where a = -3, b = 2 and c = 1.  Is the parabola concave up…

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Q: Find the point on the hyperbola xy = 8 that is closest to the point (3,0)

A: Given: xy=8 so, y=8x now any point of given hyperbola can be written as x,8x so, let's that point on…

Q: y? = t2 – 2t and x = t + 2 is I. Ellipse II. Circle III. Parabola IV. Hyperbola

A: topic - conics

Q: Given the general form of a parabola x2+6x-8y+10=0, what is the y coordinate the focus? (round to 3…

A: Explained below

Q: 5. Identify the focus of the parabola given by y = 8x². O (0,) O (-8,0) O (0,0) O (8)

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Q: Find the greatest and smallest values that the function f(x,y) = 4xy takes on the ellipse x +2y² = 1…

A: Let's find.

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: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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Q: It is true that the vertex is halfway between tje focus and the directrix on the principal axis

A: Yes, the vertex is halfway between focus and the directrix on the principle axis

Q: for the given audratic equation determine, i- which way the parabolla opens ii- the cordinate of…

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Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus :…

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Q: 4x + y2 + 8y + 8 = 0   If it is a parabola, find the vertex, focus, and directrix.

A: As a first step we will convert the equation in the standard form of equation representing a…

Q: Graph: x2 + 4y2 + 10x + 24y + 45 = 0. Where are the foci located?

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Q: F. dr, where C is the ellipse (x + 3)² + 5(y – 2)² = 16 and F(r, y, z) = x²i +y²j+ z²k.

A: The vector field is Fx, y, z=x2i+y2j+z2k. The curve C is x+32+5y-22=16. Obtain the parametric…

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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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: 5y=4 How would I make this into y=mx+b and graph this?

A: Consider the given equation,5y = 4Convert the above equation in form of  y = mx + b,

Q: Find an equation of the parabola that satisfies the conditions. a) Focus (0, -) and directrix, y =…

A: Given  Focus (0 , -1/2)  Directrix ,y = 1/2   Equation of parabola with focus at (x0 , y0) and…

Q: Find the coordinates of the four points at which the hyperboloid of one sheet given by x2 y? + 16 z?…

A: This question is related to 3D coordinate geometry, We will solve it using given information.

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: F. dr, where C is the ellipse (x + 3)² + 5(y – 2)² = 16 and F(x, y, z) = x²i+ %3D Pj+ z°k.

A: Given: x+32+5y-22=16 Fx,y,z=x2+y2+z2

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 figure below shows a lamp located three units to the right of the y-axis and a shadow created by…

A: Here we need to calculate equation of tangent line on given ellipse which passes through (-5,0)  If…

Q: Which of the following represents a parabola with vertex at (4, -2) and focus at (4, 4)? O A. (x -…

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Q: Find an equation of the parabola deseribed. Focus at (5, 0); vertex at (0, 0) O y = 20x2 O x = 20y O…

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Q: Evaluate f.y ds where C is the upper half of circle x? +y² = 9, traversed in the counterclockwise…

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Q: Evaluate x° ds where C is the part of the parabola y = x² from (0,0) to (2, 4).

A: Form the double integral and set the limits than integrate with respect to y and x.

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

A: For the solution follow the next step.

Q: Find the point on the line y = x closest to the circle of radius 1 and center (5, 2) using Lagrange…

A: First I have find the function f(x,y) and then decide the constraint.Then using Lagrange multipliers…

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: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

A: Vertices of parabolas = (0,0), Foci on the y-axis.

Q: By differentiating implicitly, find the slope of the hyperboloid 22 + y? – 22 = 1 in the x-direction…

A: We have to find slope of the hyperboloid x2+y2-z2=1 in the x-direction at the points (a) 1,2,2 (b)…

Q: Jim is running along a parabolic track where his position can be described as y = He knows that his…

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

Q: Below is the equation of a conic section such that the ordered pair (Fx, Fy) corresponds to its…

A: Given equation of the conic is 15x2-y2-210x-8y+779=0 which can written as…

Q: Determine the type of conics for each equation using the discriminant. 27. y2-x-10y -3 0 28. x2-2y2…

A: Solution is given below:

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

A: Make equation of parabola

Q: Find an equation of the hyperbola that has foci at (-10, 0) and (10, 0), and asymptotes y = 7x and…

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Q: 2. Find the equation of the hyperbola whose asymptotes are perpendicular to the lines 5x – 4y +9 = 0…

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