A conic section is said to be circle if the eccentricity e = 1. Select one: O True O False

Q: Problem The Circle xiy² a? is rotated about the x- ascis, find the Jolume of the Solid geverated 2.

A: Find the attachment

Q: Show that the graph of the equation r = 2a sin θ, a > 0, is acircle of radius a with center at…

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Q: Write the equation of Spheres with radius R.

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Q: The :. conic section xy a constant .identify (25+ w2) =D2C+ w is

A: The given equation is xy=2x+5y-25+w2, where w is a constant.   We have to identify the type of the…

Q: The center of a ceiling fan is at (2, 8). If the radius is 12in, what equation represents the outer…

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Q: The graphs of the conics intersect at two points. x² + y? = 9 = 1 4 What are the coordinates of…

A: To find the points of intersection ,first we find y2 from the two given equations and by  equating…

Q: write the equationns of the curves enclosing a reigon such that when it is rotated aboutthe x-axis,…

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Q: Which of the following conics has an eccentricity greater than 1? * 9x² + 16y² 36x +96y +36 = 0…

A: The eccentricities of conic sections are as follows. For circle e=0 For parabola e=1 For ellipse…

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

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Q: Given ellipse 9x2 + 16y2 - 144 = 0. Determine the length of arc in the first %3D quadrant.

A: Explained below

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: Find the eccentrici ty, foci, and directrices of the hyperbola y2 - x? = 4.

A: We have to find the eccentricity, foci and directrices of the given hyperbola y2-x2=4.

Q: The equation of a family of circles with center (2,k) and radius r that is tangent to the x-axis is?

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Q: Set up and simplify (but do not evaluate) : 3x ds, where C is the arc of the circle r2 + y² = 4 from…

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Q: Use the arc length formula to find the length of the curve y = 5 - 4x, -15 xs 3. Check your answer…

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Q: A family of circles with centers at the origin are described by which of the following equations?

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Q: In each part, find the standard equation of the sphere that satisfies the stated conditions. (a)…

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Q: Without graphing, how are the graphs of the following conics different? Explain.   r =1/( 1 + sin θ…

A: Given polar equations are r=11+sinθ and r=11-sinθ.

Q: Write the equation of the circle in general form that will satisfy t conditions. C. 25. Center 5:4,…

A: Given that: 28. Line segment joining (0, 7) and (-6, -3) is a diameter.30. Center is at (0, -9) and…

Q: Find the standard equation of the circle which satisfies the given conditions. 4. center at the…

A: The objective of the question is determine the standard equation of circles.

Q: 1-sketch the following hyperboloid z² – x² – y² = 1 %3D

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Q: State whether the given equation defines an elliptic paraboloid, a hyperbolic paraboloid, or an…

A: 3x2-7y2=z On simplification, we get ⇒z=x213-y217⇒z=x2132-y2172⇒z=x132-y172

Q: A circle with radius 2 contains the point (1,-4). Which of the following equations best describes…

A: The given point is 1, -4The radius is 2

Q: Calculate the distance on the ellipsoid if the distance on the secant is 18267.46

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Q: Which of the following is the cross-section of this solid?

A: Find the cross section area

Q: Graph the following conic section, identify the vertices, foci, directrices, and asymptotes (if they…

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Q: Consider the circle with center (0, 0) thát passes through the point (6, 4). Find the radius of the…

A: Given,          Consider the circle with center 0,0 that passes through the point 6,4.

Q: 1. The point (3V2, 3/2) centered at the origin. lies on a circle Whet is the oirele2 Show

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Q: which conic was Euclid's favorite and why?

A: The four types of conic sections are a. Ellipse b. Parabola c. Hyperbola d. Circle

Q: Circle to the center of C is a origin Coordina tes and radius 4

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Q: State whether the given equation defines an elliptic paraboloid, a hyperbolic paraboloid, or an…

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Q: Which conic section is represented by the equation 9a? + 4y? = 36. O Parabola O Ellipse O Circle O…

A: Standard form of an ellipse is defined by : x-h2b2+y-k2a2=1.

Q: Janiah can throw a softball in a perfect parabolic arc which is 70 feet, if Janiah does not feel…

A: Given that:-  Janiah can throw a soft ball in a    perfect parabolic arc             pitcher…

Q: In each part, rotate the solid figure about the origin exactly onto the dashed figure. If this is…

A: We want to check whether we get the dashed figure on rotating the given figure marked in blue…

Q: 2. Find points P and Q on the parabola y = 1 – x? so that the triangle ABC formed by the r-axis and…

A: Given:  To find points P and Q on the parabola y=1-x2 so that the triangle ABC formed by the x‐axis…

Q: Which of the following conics has an eccentricity greater than 1?

A: The general form of the conic is given by: Ax2+Cy2+Dx+Ey+F=0 Condition for deciding what the conic…

Q: If the semi-major and semi-minor axes of a spheroid are, a = 6 378 300 m; and b = 6 356 580 m.,…

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Q: The equation of circle C is (x+3)^2+(y-8)^2%3D36. What is its radius (h,k)? *

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Q: Evaluate (² + y2) ds, C is the top half of the circle with radius 2 centered at (0,0) and is…

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Q: Find the center (h, k) and the radius r of the circle 4x2 + x + 4y? + y – 10 = 0.

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Q: Find apolar equation for the circle x² + (y - 3)? = 9. 2

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Q: If radii of director circles of =1 and a? a? b? =1 are 2r 7.9 and r respectively and ee and en be…

A: Introduction :

Q: In the conic section r2 36y, what is the distance between the focus and the center? %3D 0 6 O 12 O…

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Q: Write the equation of the circle. Center at (-7, 11), radius 8 O (+11)² + (y-7)² = 121 O (x + 7)² +…

A: We have to find the equation of the circle which has  centre at   ( -7, 11)  and  radius 8. Now as…

Q: The length of the latus rectum of a hyperbo is equal to 18 and the distance between the foci is 12.…

A: Here, given that the conjugate axis is parallel to the y-axis. So, the equation of the hyperbola is…

Q: 2. 3x + 5y? - 6x – 20y + 25 = 0

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Q: graph the conic with the formula r=4/4+2cos(theta)

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Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.