4. Given an equation of a conic in polar formr= f(0), substituting (0 – a) results in a (clockwise/counterclockwise) rotation about the origin if a > 0. The rotation is (clockwise/counterclockwise) if a < 0.

Q: Sketch the conic section 9x² +4y² 36x + 8y + 4 = 0 Be sure to identify any of the following items…

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

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Q: 9. Explain in your own words how to decide what kind of conic it is if you have the equation Ax? +…

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Q: Show that the image of the hyperbola x² - y² = 1 is the transiscate p² = cos24.

A: Introduction: An hyperbola is another significant conic section. It has Cartesian as well as polar…

Q: 2) Foci: (2, –5 + V61), (2, –5 – V61) 20 5 Asymptotes: y ==x- 6 3 y-- 5 10 ソ=ーーX 6 3

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Q: Perform a rotation of axes to eliminate the xy-term, and sketch the graph of the conic.4x2 + 2xy +…

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

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Q: y? – 4y + 4x 16 = 0 is the equation of a conic. Write the standard form of that conic. |

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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: Find the slope of the line tangent to the conic section 25 (x+3), (y+2)² = 1 at (3,8). 36

A: We find the slope of tangent to the given conic with the help of calculus .

Q: Identify the type of conic from the discriminant.Xy-2 = 0 , =45

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Q: 1- Sketch the following conic sections: a 0 2 -4y+8 -4x2 =

A: We have to sketch the following conic section

Q: Identify the conic represented by equation x2 - 2xy + 3y2 + 2x + 4y - 1 = 0 without using a rotation…

A: if ab is greater than h^2 then conic is ellipse.

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: 1-Sketch the following conic sections: y2 - 4y +8- 4x2 = 0

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Q: -9 81 -2 9 8 7 6 Which best represents the equation of the graphed conic section?

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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: 5x 2 − 3xy + 4y 2 − 8x + 10y − 64 = 0 represents a non-degenerate conic Determine the type of…

A: Sign of discriminant i.e. B2-4AC determine the nature of non-degenerate conic.

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

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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: Identify the type of conic from the discriminant.x2+2ry +y2 + V2x-V2y-2=D0, =45°

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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: 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: 2. Suppose that the equation Ax + Bxy + Cy + Dx + Ey + F = 0 represents a conic section…

A: Suppose that the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 represents a conic section…

Q: (b) If the conic is rotated counterclockwise about the origin through an angle 3n/4, write the…

A: If the conic is rotated counterclockwise about the origin through an angle 3π4 then write the…

Q: A general equation of conic section is given as y + 4x + 4(x – 2y) + k =0. Determine the value/s of…

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Q: Determine the equation of the given conic in XY-coordinates when the coordinate axes are rotated…

A: Since,  This implies,  Since the coordinate axes are rotated through  , so equation of x and y can…

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: Determine the equation of the given conic in XY-coordinates when the coordinate axes are rotated…

A: Given: The equation of the conic is given as, And the indicated angle is given as,

Q: Perform a rotation of axes to eliminate the xy-term, and sketch the graph of the “degenerate”…

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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: Perform a rotation of axes to eliminate the xy-term, and sketch the graph of the “degenerate”…

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Q: Is it true or false that the coefficients of first order terms of the conic Ax? + Bry+ Cy² + Dx +…

A: Consider the provided question, To write the general second degree polynomial equation Ax2 + Bxy +…

Q: Identify and sketch the graph of the conic section.y2 + x = 0

A: On simplification, we get

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

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

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Q: The equation for the conic section with focus (x, y) = (c, 0), direc ricity e 1, by choosing c =…

A: Topic:- geometry

Q: Identify the type of conic section from the equation: y^2 - 4y - x^2 6x =12

A: We have been given the equation  y2-4y-x2+6x=12

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: 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: 3. Suppose we have Conic described by 2nd-degree equation in the plane : 9y2 + 4x2 = 16 a. Find the…

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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: For numbers 1 and 2: Choose the graph that corresponds to the given equation of the conic. 1. (x –…

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