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

Q: The x-axis and the y-axis are asymptotes of the equilateral hyperbola whose equation is xy = 9. Find…

A: Given: xy=9 we know that length of transverse axis and conjugate axis is equal for rectangular…

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 equation of the parabola with vertex at (0, 0) and directrix y = -8 in standard form?…

A: Given that, vertex of parabola is (h, k) = (0, 0) diretrix of parabola is, y = -8 We have to find…

Q: What is the equation for the parabola below in terms of its focus and directrix? y = _____

A: Given: equation of the parabola

Q: What is the standard form of the parabola, y + 2x + 10y + 9 = 0, given in conic form?

A: Do some rearrangement in the equation of given conic to convert it in standard form of equation

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

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Q: Find the equation for the parabola that has its focus at the (−394,−4) and has directrix at x=−25/4

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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…

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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: Find the general equation of the parabola with vertex at the origin and focus at (-4, 0)

A: The general equation of a parabola with vertex (h,k) is (y-k)2=4a(x-h)

Q: Consider the parabola whose vertex us at (2,-1) amd focus at (0,-1). What is the general form of the…

A: Given, The vertex of the parabola = 2, -1  Focus of the parabola = 0,-1 We have to write the general…

Q: Find the equation of a parabola having directrix y = -5.

A: if given equation of the directrix y= -a then equation of the parabola is  x^2 = 4ay

Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: Find the equation of the parabola with focus at (5, 0) and directrix x = −5.

A: Focus lies on x-axis.

Q: Find the equation of the tangent to the hyperbola x2 - 4y2 = 9 at (5, 2).

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Q: Find the equation for the parabola that has its vertex at the origin and the focal point is 278…

A: Consider the equation of parabola vertex at origin and focus to the right of directrix. y2=4ax…

Q: Find b and c so that the parabola with equation y = 4x2 - bx - c has a vertex at (2 , 4)?

A: Using the vertex formula we find the x value of the vertex[formula: x value of vertex of Ax^2+Bx+C=0…

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

A: Given: Focus on the negative y-axis, 6 units away from the directrix

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus :…

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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: Write an equation for the hyperbola which has foci at (0, v5) and (0,-V5 and asymptotes at y = ±3x.

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Q: Given the general form of a parabola x2+8x-12y+11=0, what is the equation of the directrix? y=_____.…

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Q: Determine the equation of the parabola given the focus at (-10,23/2) and directrix at y=-11/2.

A: Given- Focus -10,232 and directrix y=-112 To Find- The equation of the parabola.

Q: find the equation of the parabola with the given  Focus (2, 0), directrix x = −2

A: Our Aim is to find the equation of the parabola with the given Focus (2,0) and directrix x=-2.

Q: 1. For the parabola equation: (y-2) = -3(x+4)^2 + 7, in which direction does the parabola open? *

A: We have to find the direction in which the given parabola opens.

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: The equation x2- x   y + y 2  = 3  represents a “rotated ellipse,” that is, an ellipse whose axes…

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Q: Find the standard form of the equation of the parabola. Focus at (0, 4), directrix y = -4

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Q: Find the equation for the parabola that has its vertex at the origin and has a focus at (18.1, 0).…

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Q: What is the equation of the parabola shown below, given the focus at F(1, 5) and the directrix x =…

A: Here we have to find the equation of the parabola, vertex, and equation of the axis of symmetry of…

Q: d the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter DNE.)…

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Q: Find the standard equation of a parabola if its latus rectum measures 9 units, axis at y = 3, p is…

A: Let's find standard equation of a parabola.

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

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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: Fid the equation of the tanget to the parabola  x2 - 22x + 24y +169 = 0 at  the point whose focus…

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Q: help in 30mins pls

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Q: 1. Marsha was completing the steps for a parabola that has a focus at (5,-2) with directrix at y =…

A: Formula:-1)Distance between two points (x1,y1) & x2,y2 is d=(x1-x2)2+(y1-y2)22)Distance of a…

Q: What is the equation of the parabola with a vertex at (4.8) and a directrix at y = 53

A: This is a simple question based on conic section (Topic is parabola) before attempting this question…

Q: Write an equation for the hyperbola that has foci at (0, v65) and (0, - v65), and asymptotes y =…

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Q: Find the equation of a parabola whose focus is at(2,-3) and directrix's equation is x=5.

A: Distance between the point x1 , y1 and a lineax+by+C=0 is ax1+by1+Ca2+b2

Q: Find the equation of a parabola that has focus at (-4,0) and directrix 2

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Q: Find the equation for the parabola that has its vertex at the origin and has directrix atI = 27…

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Q: 4) Find the equation of a parabola which has the focus at (2,9) and the directrix at x=10.

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Q: Find the equation for the parabola that has its focus at (-53/4, -7) and has directrix x = 5/4.

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Q: Find the equation of the parabola whose vertex lies at (0,-2) and directrix at x=2

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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: The focus of a parabola is (-3,5) and the directrix is y = -1. Which equation represents a parabola…

A: Given: the focus of a parabola -3,5 and the directrix is y=-1 Formula: Distance between point x,y on…

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.