Find the vertex, focus, and directrix of the parabola. Then sketch the parabola. x + y? = 0 (x, y) = (| vertex focus (x, y) = directrix

Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 1) and directrix…

A: Given that Focus of parabola is F0, 1. Directrix is y=-1. We have to prove that y=14x2 is the…

Q: Find an equation for the parabola with focus (4, 0) and directrix x = 3. Sketch the parabola…

A: Given that the focus of the parabola is (4, 0) and its directrix is x = 3. Observe that the focus…

Q: Find the vertex, focus, and directrix of the parabola. y² + 2y + 16x + 33 = 0 (x, y) = vertex focus…

A: The given equation of parabola is:             y2+2y+16x+33=0⇒ y2+2y+1+16x+32=0⇒…

Q: 1. Consider the parabola with focus point (1, 1) and directrix the horizontal line y = -3. a) What…

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Q: Give the equation of the parabola with focus F (0; 2)  and directrix y = -2 . Give an equation of…

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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: Find the standard form of the equation of the hyperbola satisfying the given conditions. Endpoints…

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Q: Find the vertex, focus, and directrix of the parabola. x2 = 5y vertex (x, y) = ( (x, y) = ( focus…

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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 the standard form of the equation of the parabola with the given characteristics. Directrix: y…

A: Standard form of equation of parabolla is given by :x-h2=4ay-kThe distance between 0,2&8,2 is…

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

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Q: Find an equation of the parabola that has a focus at (2, 16) and a vertex at (2, 8): Y = Find an…

A: Parabola is a U-shaped curve and it is part of a conic section.  The focus of the parabola is the…

Q: Determine an equation for the parabola with focus (3,2) and directrix y = -4. %3D

A: Given problem is :

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: Find the equation of a parabola that has focus at (−4,0) and directrix x=2

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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: The Dufferin Gate is a parabolic arch that is approximately 20 m tall and approximately 22 m wide.…

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Q: 광y-6x +2=0

A: Property of parabola

Q: Find the vertex, focus, and directrix of the parabola. Then sketch the parabola. x2 + 16y = 0 (х, у)…

A: To find the vertex , focus and directrix of the given parabola.  x2 + 16y = 0

Q: Find the focus, directrix, and focal diameter of the parabola. x² + 9y = 0 focus (x, y) = directrix…

A: topic-parabola

Q: Find the standard form of the equation of the hyperbola satisfying the given conditions. Endpoints…

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Q: Find the focal diameter of this equation:   y^2=32x   also sketch a graph of the parabola and…

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Q: Find the focus and directrix of the parabola given by x2 = -8y. Then graph the parabola.

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Q: Find the parabola's focus and directrix. Then sketch the parabola. x = 16y %3D

A: The standard form of parabola is x2=4ay. Now focus of this parabola is given by     (0,a) and…

Q: ind the equation of the parabola with focus of (1,-1) and directrix of x=3.

A: Explanation: Given that,  Focus is (1,-1)  Directrix: x=3   To find the vertex of the parabola, we…

Q: Find the focus and directrix of the parabola given by x2 = -12y.Then graph the parabola.

A: The given equation of parabola, x2=-12y The equation is of the form x2=4ay,  Compare both the…

Q: What are the focus and directrix for the graph of the parabola given: y? = 16x O focus (4,0);…

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

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Q: Find an equation of the parabola that satisfies the conditions. a) Focus (0, -) and directrix, y =…

A: Given  Focus (0 , -1/2)  Directrix ,y = 1/2   Equation of parabola with focus at (x0 , y0) and…

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

A: Solution: Consider the equation of the parabola: x-32 = 12y+1 Therefore, it can be rewritten in the…

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: Given:

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

A: The equation of parabola:

Q: Find an equation of the parabola in standard form with focus at (3,0) and directrix x=-3

A:

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

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Q: Focus: (-10,0);Directrix: x =25.Find the standard form of the equation of the parabola satisfying…

A: the given conditions are: focus:(-10,0) and directix: x=25 we have to find the standard form of the…

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

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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: A parabola has a focus located at (6,) and a directrix of y= 4. %3D What are the coordinates for the…

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Q: Find the parabola's focus and directrix. Then sketch the parabola. 2= - 8y %3D

A: The standard form of equation of parabola is (x-h)2=4p(y-k) where (h,k) is the vertex. The focus of…

Q: 10.5

A:

Q: Find the vertex, focus, and directrix of the parabola. Then sketch the parabola. y? + 6y + 8x + 25 =…

A: Solution: 1st 3 sub parts

Q: Find the focus, directrix, and focal diameter of the parabola: x2 = -8y Focus: F( Directrix: Focal…

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Q: Find an equation of the parabola with focus (-1,-4) and directrix x=1

A: We can find the equation of parabola as below.

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.