Highway engineers design a parabolic curve for an entrance ramp from a straight street to an interstate highway. Find the equation of the parabola in standard form using a focus and directrixr.

Q: Give the equation of the directrix of the parabola with the equation x= - (v+3)². Blank 1 Blank 1…

A: Given query is to find the equation of the directrix for the parabola.

Q: Find the vertex, focus, and directrix of the parabola. Sketch its graph, showing the focus and the…

A: Consider the provided parabola, 20x=y2 Find the vertex, focus, and directrix of the parabola. Sketch…

Q: Write the equation of a parabola in standard form from the following information: Focus (-5, 7)…

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Q: Write the standard form of the equation of the parabola with the given directrix and the vertex at…

A: Topic-parabola

Q: Use the tenation provided to write the stondar form equation of each ellipse.

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Q: write the equation of a parabola whose directrix is x = 5.75 and has a focus at (12.25, 5).

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Q: Find the focus and directrix of the parabola given by y2 = 8x.Then graph the parabola.

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Q: What are the coordinates of the focus of the parabola (y + 5) = -8(x – 4) Enter your answer by…

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Q: Find the standard form of the equation of the parabola with the given characteristics. focus: (8, 8)…

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Q: Write the equation of a parabola whose directrix is æ 0.25 and has a focus at (1.75, 6)

A: Given, The parabola whose  Directrix is x = 0.25 Focus at 1.75, 6  We have the write the equation…

Q: Find an equation that models the path of a satellite if its path is a hyperbola, a = 55,000 km, and…

A: The standard equation of hyperbola with center (0,0) and having horizontal transverse axis is given…

Q: Write the standard form of an equation of an ellipse subject to the given conditions. Major axis…

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Q: For Exercise, find the standard form of the equation of the ellipse or hyperbola shown.

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Q: Find the standard form of the equation of the parabola with the given characteristics. Focus: (2,…

A: Given that the directrix is x = -2, we can conclude that the parabola opens to the right(in a…

Q: Find the focus and directrix of the parabola given by y2 = 12x. Then graph the parabola.

A: y2=12x Now comparing with y2=4ax, we get 4a=12⇒a=3 Therefore focus is, a, 0=3, 0 & directrix is,…

Q: Use a graphing device to graph the ellipse.

A: We have to draw the graph of ellipse: x2+y212=1 We know the standard form of equation of ellipse,…

Q: Find an equation that models the path of a satellite if its path is a hyperbola, a = 55,000 km, and…

A:

Q: Write the equation of a parabola whose directrix is y = - 0.75 and has a focus at (– 8, 8.75).

A: Let's find.

Q: Determine the equation of the parabola using the given information. Focus (0, −3) and directix y =…

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Q: Identify the directrix, focus, and vertex of the parabola in the figure.

A: Given that: Graph of parabola.

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

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Q: Write the standard equation of parabola with the focus at (-1, 2) and the vertex (1,2) Determine :…

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Q: Find a Cartesian equation for the curve and identify it as either a hyperbola, circle, limaAson,…

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Q: Find the standard form of the equation of a parabola with focus (8,0) and directrix x = -8.

A: Focus is, a, 0=8, 0⇒a=8 Directrix is x=-8.

Q: Write the Equation of the parabola: Focus: (0,5), Directrix: y= -3

A: We have to find the equation of parabola

Q: Write the equation of a parabola whose directrix is æ = 4.5 and has a focus at (13.5, 4). Preview

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Q: Find the standard form of the equation of the parabola with the given characteristics.   focus:…

A: If (a,b) is the focus of the parabola,  and directrix is y = k,then strandard equation of parabola…

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

A: The equation of parabola:

Q: NSWER. a. Find all the parts of the ellipse and plot ellipse with the equation.

A: Introduction: An ellipse is a closed curve defined by its foci and stretched shape along its…

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 focus and directrix of the parabola y = -x2, and sketch the graph.

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Q: Find an equation of the parabola with focus (-6, -3) and directrix x= 4. ロ=ロ

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Q: Find the standard form of the equation of the parabola with the given characteristics. focus: (5, 5)…

A: Answer and explanation is given below

Q: . All parabolas with x-axis as the axis and (a, 0) as focus.

A: In this question, concept of differential equation is applied. Differential Equation A differential…

Q: Find an equation of the parabola with focus (4, 4) and directrix x=0.

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Q: 1. Olympic Stadium in Montreal, Canada was constructed in the shape of an ellipse with major and…

A: Major axis = 480 mMinor axis = 280 m

Q: Write the equation for a parabola with a Focus (4,1) and Directrix y=8 ?

A: we know that the distance between any point on parabola and the focus is same as the distance…

Q: Write the equation of a parabola in standard form from the given information Focus at (-5,7)…

A: Since , focus lies on x-axis Therefore , equation is either y2=4ax or y2=-4ax Now focus has negative…

Q: the focus of the parabola and the directrix

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Q: Find the standard form of the equation of the parabola with the given characteristics. Focus: (1,…

A: Given: A rough sketch of the parabola shall be as follows:

Q: Find the focus, directrix, and focal diameter of the parabola y = x², and sketch its graph.

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Q: As viewed from above, a swimming pool has the shape of the ellipse given by x? + 1600 900

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Q: Write the standard form of an equation of a parabola with focus (1, 6) and directrix y = −2.

A: Given that focus and directrix of parabola.Find the equation of prabola in standard form.

Q: Find the vertex, focus, and directrix for the parabola (x−1)2=−8(y−3)

A: Vertex form of parabola :  y = a( x - h)2 + k

Q: Find the focus diretrix, and focal diameter of the parabola: x^2=-8y

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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: Find the vertex, focus, and directrix of the parabola (x − 6)2 − 2( y + 7) = 0, and sketch its…

A: Given: The equation of the parabola is, x-62-2y+7=0 The above equation can be converted into vertex…

Q: Find the vertex focus focal width and equation of the axis for each parabola. y^2+8y+4-6x+0

A: Given: y2+8y+4-6x=0 for finding given values, first we convert given equation in standard form of…

Q: Determine the equation and sketch the graph the parabola given focus at (12, 3) and directrix at x =…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.