Match the parabolas in Exercises 1-4 with the following equations: x? = 2y, x2 = -6y, y? = 8x, y? = -4x. Then find each parabola's focus and directrix. 1. 2. 3. 4. х

Q: Find the standard equation of the hyperbola. Two corners of auxiliary rectangle at (−4 ,−7) and (0…

A: Given: The two corners of the auxiliary rectangle of a hyperbola are at -4,-7 and 0,0 and transverse…

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: For Exercise, determine whether the transverse axis and foci of the hyperbola are on the x-axis or…

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Q: Find the standard form of the equation of th parabola with: and Focus (-2, 6) Directrix X = 8

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Q: What is the standard equation of the hyperbola if the length of its conjugate axis is 10 v5 and one…

A: To find- What is the standard equation of the hyperbola if the length of its conjugate axis is 105…

Q: What is the equation of a parabola with focus at (2,6) and directrixx = 8? %3D O y - 12y + 12z – 24…

A: Equating distance from directrix to distance from focus gives equation of parabola.

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: Find the equation of the hyperbola with center (o, o), a vertex at (5, o) and an extremity at (o,…

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Q: Find the standard equation of the parabola which satisfies the given condition. Focus (7, 11),…

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Q: What is the directrix of the parabola? (x + 3)² = 8 (y – 1) y = 3 O y = 2 O y = 1 O y = -1

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Q: 2. Which equation represents the parabola with focus (1, 4) and latus rectum of 4? Oy = 4(a- 1)2 + 3…

A: Here, the parabola is of the form (x-h)2=4a(y-k) Whose focus is given by (h,k+a)=(1,4) given…

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

A: equation of parabola:-

Q: Which is the standard equation of the hyperbola centered at the origin, with a vertical transverse…

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

A: Given:Vertex=0,0Directrix y=-3Equation of parabola:x-h2=4py-k

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

A: First we have to calculate distance from directix to vertex. I.e P Then insert values of center and…

Q: What is the standard equation of the hyperbola if the length of its transverse axis is 12 and one of…

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Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 3.

A: Given :          The equation of directrix of the parabola is x + 1 = 0          The length of the…

Q: Given hyperbola   (y + 1)2   −   (x − 2)2   = 1       9                4         what will its…

A: Given: An equation of the hyperbola, y+129-x-224=1.

Q: 2. what is the general equation of a parabola that opens upward with v(-1,2)?

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: What are the coordinates of the vertices of the hyperbola whose equation is given by 4y2 – x² = 4? A…

A: The given hyperbola equation,        4y2-x2=4

Q: For Exercise, an equation of a hyperbola is given. Determine whether the transverse axis is…

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

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

Q: ises 17–30, find the equations of the parabola

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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: what is the equation of a parabola with a vertex at (4, 8) and a directrix at y=5

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Q: What is the equation of the parabola in general form given its vertex at (-1,-5) and focus at…

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

A: Here we find the equation of parabola.

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

A: Given- The parabola that has its vertex at the origin and satisfies the given condition(s).…

Q: What is the equation of the parabola with vertex at (0,0) and focus (0, –4) in standard form?…

A: see below the calculation

Q: For Exercise, an equation of a hyperbola is given. Determine whether the transverse axis is…

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Q: 2. Write the general equation of the parabola with directrix at x FG,-1), and v (. -1). 2

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Q: 21. What's the standard form equation of a parabola with directrix x = -10 and focus (10,0)?

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Q: Find the standard form of the equation of the parabola with the given characteristics. Focus: (0,…

A: The equation of parabola:

Q: 4. Label the focus, directrix, and vertex on the graphs given for the parabolas in Exercises 2 and…

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Q: Which is the corresponding equation of the hyperbola with foci located at (-8, 0) and (8, 0) and a…

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

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Q: Find the standards form of the equations of the below parabolas with the given characteristics.

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Q: Determine the standard equation of the parabola opening upward, with focus at (0,6) and whose length…

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Q: What is the standard form of the equation of the parabola with the focus (-3, 6) and the directrix y…

A: GIVEN: focus (-3, 6) Directrix y = -2

Q: What is the Equation of a Parabola with directrix x = 3/2 and focus (5/2 , 4)

A: The given problen is solved below in detail.

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

A: Explanation:

Q: For Exercise, write the standard form of an equation of a hyperbola subject to the given…

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Q: Find an equation in standard form for the hyperbola with foci at(+8, 0), transverse axis with length…

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Q: What is the equation of the directrix of a parabola having vertex at (4, 3) and focus which is 2…

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Q: What is the standard form of the equation of the parabola with the focus (6, –1) and the directrix I…

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Q: What is the equation of the parabola with vertex at (0, 0) and directrix y = 3 in standard form.…

A: Given vertex 0,0 and directrix y=3. We have to find equation of parabola.

Q: Which is the equation of a hyperbola with co-vertices at (0, 7) and (0, −7) and a transverse axis…

A: Ans (1) we have givenCo=Vertics of hyperbola (0,7) and (0,-7)⇒Compairing with co-vertice from (0, ±6…

Q: Which is the corresponding equation of the hyperbola with foci located at (−8, 0) and (8, 0) and a…

A: Given data is : Foci are -8,0 and 8,0 The transverse axis is 14 unit

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…