Given an ellipse with the implicit equation: (x - 4)2 + (y + 5)? = 1 36 we can rewrite it using the parametric form: x = h + a cos(t) y =k+b sin(t) Fill-in each of the 4 blanks below for h, then a, then k, and then b. (Enter only integers, please!) 4. A cos(t) 9. 5 A sin(t) 1

Q: Зл The parametric curve x = 7 sin 2t and y = 9 cos 2t, where , traces the ellipse 49 = 1 81 a. 3…

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Q: A cheetah can run at 105 feet per second, but only for 7 seconds, at which time the animal must stop…

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Q: x + xy + y? = 9 %3D sa slanted ellipse illustrated in this figure: 1 – 4 -2 2.

A: Given that x2+xy+y2=9 Differentiate w.r.t x , 2x+y+xy'+2yy'=0 y'=-2x+yx+2y Now, differentiate w.r.t.…

Q: The equation x2-xy+y2=1 describes an ellipse. Find the coordinates (x,y) of all the points on the…

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Q: d. P = 4x1 – 2x2, Q = 2x1 + 6x2; D is the interior of the ellipse: x1 = 2 cos 0, x2 = sin 0, θε [-π,…

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Q: 8. Give a parametric representation of the given ellipse with the orientation clockwise. x2 y? -=D1…

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Q: Describe the graph of the equation. r = 10 cos ti + 3 sin t j – k O Itis an ellipse in the z = -1…

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Q: Given the general form of all the conic sections: Ax + By + Cx + Dy+ E = 0 Choose what has to be…

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

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Q: Given the following conic section, determine its shape and then sketch its graph. 52? + 4y? + 3х +…

A: Since the coefficient of x2 and y2 are different and they both have positive signs, so it is an…

Q: A 10-ft ladder slides down a wall as its bottom B is pulled awayfrom the wall (Figure 20). Using the…

A: A 10-ft ladder slides down a wall as its bottom B is pulled away from the wall. It forms angle θ as…

Q: Given the parametric equations, x = 2t + 5 and y = 3t2 - 1, find the point on the graph at time, t =…

A: We can find the point as below

Q: = 1 10 12 = 1 20 12 x2 = 1 100 36 =1 100 144

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Q: ne ellipse 52 1 can be drawn with 22 ritten in the form [t) = r cos(t) with r = nd y(t) =

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Q: State the equation of the parabola which has a focus of (9, 3) and a directrix of y = -3. (Let a be…

A: To find the equation of the parabola having focus and a directrix, let we choose (x, y) be any point…

Q: Given the parametric equations, x = 2t + 5 and y = 3t2 - 1, find the point on the graph at time, t =…

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Q: Determine the equation (both standard and general) of the following conic sections based on the…

A: To find the equation of the conic sections with the given conditions

Q: Given the following conic section, determine its shape and then sketch its graph. a – 2xy + y² +x –…

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Q: The asymptotes of the graph of the two given parametric equations are 1 and y = x = t+1

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Q: 26. Find the standard form of the equation of the specified ellipse. Foci: (1, 5), (-3, 5); Major…

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Q: A lizard moves through the plane with its position at t seconds given by the parametric equations…

A: parametric equations x=3cos(2pi t)+2, y= -6cos(2pi t)+1.

Q: Determine the equation of the directrix of the following conic section: y? = -18a O y = -9/2 O x =…

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Q: 17 Select the conic section represented by the equation. 4x 2 -y 2 + 24x + 4y + 28 = 0. circle…

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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: The equation x2 − xy + y2 = 3 represents a “rotated ellipse”, that is an ellipse whose axes are not…

A: Given: The equation x2 − xy + y2 = 3 represents a “rotated ellipse”, that is an ellipse whose axes…

Q: Identify the conic section given by the following equation. æ? + 30x – 4y? – 168y – 1639 - Select…

A: Please refer the attached image for complete solution.

Q: Determine what type of conic section corresponds to the given equation. (3x + y)² – 2y = x Ellipse.…

A: We have to check the given equation.

Q: Find parametric equations for an object moving clockwise along the ellipse 25 =1 beginning at (0,4)…

A: For the solution follow the next step.

Q: Consider the equation of an ellipse written in terms of x and y as 13 z? + 8 yz + 7 y² = 1 a. Find…

A: Note:- For a non singular square matrix A,  A = PT D P  Here, P is orthogonal matrix that is, P-1 =…

Q: 21 Find the equation for the parabola that has its focus at the 2 and has 4 11 directrix at æ = 4…

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Q: Prove that the graph of the equation Ax2 + Cy2 + Dx + Ey + F = 0 is one of the following (except in…

A: Given, The graph of the equation is, Ax2+Cy2+Dx+Ey+F=0 Let A=1, C=0 so that, x2+Dx+Ey+F=0 By…

Q: Find the equation of the following conic in GENERAL form. 1. Circle that is tangent to the lines…

A: Consider the equation of the circle is x-h2+y-k2=r2 where h, k is the centre and r is radius. It is…

Q: 8. Find the longest and the shortest distances from (1, -2) to r? + 2y? = 1. 9. Try to solve problem…

A: Distance formula=Sqrt{(x-x1)^2 +(y-y1)^2} The Lagrange method of multipliers is  F(x,y)=f(x,y)+lamda…

Q: Use the following conic sections to answer: x? – 2x + 2y? – 8y +7 = 0 a. Graph the conic section b.…

A: Consider the given equation:…

Q: 1-Sketch the following conic sections:. ,2-4y+8-42 0 b- y2 -4y-4x2 -8 3 -s)2 -7(*+1 -1 a- C-

A: Since you have posted multiple questions we solve the first three sub parts of first question for…

Q: The ellipse x2 42 1 62 can be drawn with parametric equations. Assume the curve is traced clockwise…

A: Substitute x=4cost in x242+y262=1 to find y.…

Q: (41, Ellipse:. x = h + a cos 0, y= k + b sin 8

A: Form ellipse

Q: t y = t + 1 II

A: Consider the given parametric equation: x=1tt=1xSubstitute the value of "t" in y=tt+1,y=1x1x+1y=11+x

Q: The ellipse 82 =1 can be drawn with parametric equations where a(t) is written in the form 72 2(t) =…

A: Parametric equation of ellipse is  x = a cost  y = b Sint  In this question,  a = 8 , b = 7

Q: Describe the graph of the equation. r = 9 cos ti + 2 sin tj - k O tis an ellipse in the z = -1…

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Q: 3T 2 a) When graphing the parametric equations, what are the x and y coordinates when t= b) Does the…

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Q: For an NBA regulation basketball court, the hoop is 10 feet above the ground, and the horizontal…

A: We have been given the equations of motion for each coordinate as:x=v0t cosθy=v0t sinθ-16t2+8.5 The…

Q: 15. Find an equation for the ellipse of eccentricity 2 that has the line メニZ as directrix and the…

A: Please refer the attached image for complete solution.

Q: 3. Find the equation of the following hyperbola after it has been rotated counterclockwise by : y? –…

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Q: Which is the equation of a parabola with a directrix at y = 2 and a focus at (5, 0).

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Q: 23 24-242 +13x² +3y~ =0 २१ write the stand and form -of the evuation of the ellipse Tand sketch 计" 1

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