Write the standard equation of parabola with the focus at (-1, 2) and the vertex (1,2) Determine : a) orientation b) opening c) focal length d) focal width e) equation of directrix

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

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Q: In an ellipse, the foci are at (-4, 3) and (4, 3) and one vertex is at (6, 3). How long is the major…

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Q: Give the standard equation of the parabola with focus (-3,0) and directrix x=3

A: Standard equation of parabola is y2=±4ax Given that focus of parabola is (-3,0) and directrix is…

Q: Find the standard equation of the parabola with directrix x + 1 = 0, axis y = 1 and the length of…

A: If the axis of parabola is y = 1, then the parabola is horizontal. As we know that the standard…

Q: Find the vertices, foci, and the lengths of the major and minor axes for the ellipse X + y = 1. 36…

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Q: find the equation of hyperbola with center (4,-1), transverse axis parallel to the y axis distance…

A: Given: A hyperbola with center 4, -1 , whose transverse axis is parallel to the y-axis. The…

Q: Find, in terms of x and y, the equation of the hyperbola in standard position with focus (5,0)  and…

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Q: Find an equation of the parabola with focus (7, 3) and directrix r= 1,

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Q: What is a parabola? What are the Cartesian equations for parabolas whose vertices lie at the origin…

A: What is a parabola? What are the Cartesian equations for parabolas whose vertices lie at the origin…

Q: For a hyperbola, the foci lie on a line called the_________

A: Given that, A statement, " For a hyperbola, the foci lie on a line called the ______ ."

Q: Explain why it is not possible for a hyperbola to have foci at (0, -2) and (0, 2) and vertices at…

A: The standard form of the equation of a hyperbola with center (0,0) and transverse axis on the y-axis…

Q: Find an equation for the hyperbola that satisfies the given conditions. Foci: (0, ±5), length of…

A: Given that hyperbola satisfies the following conditions: Foci=0,±5  and length of transverse axis is…

Q: Find the equation of the hyperbola having center at the origin with transverse axis on the x-axis,…

A: Given-  Hyperbola having center at the origin with transverse axis on the x-axis, a=4, and latus…

Q: Given: Foci: (2,1) (10,1) c = 4 a=? b=? Center: (6,1) Find the standard form of the ellipse

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Q: Given a parabola's focus at (6, −4) and directrix at y = −7, how would you write its equation?

A: Equation of parabola: x-h2=4py-k Where vertex is (h, k) Focus is (h, k+p) And directrix y = k - p

Q: 2. The points where a hyperbola intersects the line through the foci are called the

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Q: find the coordinates of the foci and vertices, the endpoints of the transverse axis, conjugate axis,…

A: Given:- x9/9- y2/25=1 To find:- find the coordinates of the foci and vertices, the endpoints of the…

Q: Find an equation for the hyperbola that has its center at the origin and satisfies the given…

A: We have, a hyperbola satisfies the given conditions as vertical transverse axis of length 10,…

Q: Determine the focal distance of a hyperbola if the length of the transverse and conjugate axes are…

A: The focal distance of a hyperbola is 17units.

Q: Find the Parabola with Focus (7,-2) and Directrix x=-9

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Q: Find the vertices, foci, and the lengths of the major and minor axes for the ellipse 49 = = 1. 4…

A: given x249+y24=1⇒(x-0)272+(y-0) 222=1this is  in standard form of ellipse (x-h)2a2+(y-k) 2b2=1where…

Q: The line segment perpendicular to the axis of symmetry, passing through the focus and with endpoints…

A: Given:The line segment perpendicular to the axis of symmetry, passing through the focus and with…

Q: Find the vertex, focus, and directrix for the parabola.

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Q: Determine the standard form of an equation of the parabola with focus (1, 2) and directrix x = 7.

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Q: What is the equation of the standard hyperbola with vertices at(0, ±a) and foci at (0, ±c)?

A: Given-  Hyperbola with vertices at (0, ±a) and foci at (0, ±c). To find- The standard equation of…

Q: Find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola 15.6x = y?

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Q: The distance between the vertex and the focus of a parabola is called the __________ length and is…

A: First of all, consider the definition of the vertex and the focus of a parabola.The vertex of…

Q: Find the general form and graph of the focal width of a parabola is 14 units and its vertex can be…

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Q: Find the vertices, foci, and eccentricity of the ellipse. 3x2 + 4y2 = 12 (x, y) = (| vertex (smaller…

A: 3x2+4y2=12⇒3x2+4y212=1⇒x24+y23=1⇒x222+y232=1 Now comparing with x2a2+y2b2=1, we get a=2 & b=3…

Q: What is the length of the transverse axis of the hyperbola whose foci are (0, -5) and (0,5), and…

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Q: If the directrix is horizontal, then the parabola opens (horizontally/vertically).

A: Given:We must find the missing word in the given sentence.So, Definition of parabola said:A parabola…

Q: Find the equation of Hyperbola using only the following information: Center at (0, 0) Vertices at…

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Q: 2. +y².

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Q: Determine the Vertices and Foci of the Hyperbola 9x - 4y = 36 %3D and Sketch.

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Q: 2. 3x + 5y? - 6x - 20y + 25 = 0

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Q: What is a parabola? What are the Cartesian equations for parabo-las whose vertices lie at the origin…

A: Explanation:

Q: Derive an equation for the parabola with focus (a , b) and directrix x = c

A: Given focus f =(a,b) and directrix x=c Let A(x1,y1) be any point so that  |Af|= |AD| Where Af=…

Q: How is the distance between vertices for hyperbola equal to 2a?

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Q: Find the eccentricity of a hyperbola having distance between foci equal to 18 and the distance…

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Q: What equation is used to find the foci of a hyperbola?

A: The hyperbola which is having transverse axis along x-axis is given by x-h2a2-y-k2b2=1 where h,k is…

Q: The parabola has focus (0,-2) and directrix y=2.

A: equation of parabola with focus ( a , b ) and y = c  is given as below : here a = 0 b = -2  c = 2

Q: 40. y² – 16x² + 64x 208 = 0

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Q: How is the axis of symmetry related to the vertex, focus, and directrix of a parabola?

A: See the attachment below

Q: Find the vertices, foci, and eccentricity of the ellipse. 9x2 + 49y2 = 441 vertex (х, у) %3D…

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Q: Given the following information about the hyperbola, find both its standard and general form= FOCI:…

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Q: In Exercises 5–-16, determine the coordinates of the focus and the equation of the directrir of the…

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Q: 2. PARABOLA VERTEX = (2, FOCUS = (1,

A: Given vertex=2,1 and focus=1,1 We have to find the equation of the parabola. We can see that the…

Q: Determine the standard form of the parabolic equation x = 1/2 (y + 5)2 − 2. Further, characterize…

A: x=12y+52-2 On simplification, we get ⇒12y+52=x+2⇒y+52=2x+2⇒y--52=2x--2 Now it is in the form of…

Q: What is the geometric interpretation of b/a in the equation of a hyperbola in standard position?

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Q: 3. 9x2 + 4y2-54x 16y + 97 0

A: 9x2+4y2-54x-16y+97=0