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

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

A: Given,        An equation for the parabola that has its vertex at the origin and has       it's…

Q: The focus of the parabola y^2 = 4x is at

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

A: To find  an equation for the parabola that has its vertex at the origin and satisfies the given…

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

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Q: Find the vertex, focus and directrix of the parabola given by y2 + 2y + 4x - 7 = 0.Then graph the…

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Q: Find the equation of the parabola with focus (-3, 0) and directrix x-3.

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Q: Find the vertex, focus, and directrix of the parabola x2 − 2x − 4y − 7 = 0 , and sketch its graph.

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Q: Find the focus and directrix of the parabola. 2y2 + 2x + 20y + 52 = 0

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Q: Sketch the graphs of the parabolas (a) x² = 12y (b) y² + 8x = 0 and show the focus and directrix of…

A: If we have parabola in the form of  x2 = 4ay, which is a upward parabola    Then equation of…

Q: Find an equation of the parabola that satisfies the given conditions.Vertex V(3, -5), directrix x =…

A: We know that equation of parabola is, y-k2=4px-h       ...(1) Where (h, k) is the vertex and x = h -…

Q: Find the vertex, focus, directrix, and focal width of the parabola. x2 = 28y

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Q: Consider the graph of  y = ax2 + bx + c, where a = -3, b = 2 and c = 1.  Is the parabola concave up…

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Q: Find the standard form of the equation of the parabola with the given and vertex at the origin.…

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Q: Find the vertex,focus,and directrix of the parabola given by y2 + 2y + 4x - 7 = 0.Then graph the…

A: Given:             y2+2y+4x-7=0 Parabola standard equation 4px-h=y-k2 is the standard equation for a…

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

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Q: Find an equation for the parabola that has its vertex at (1, 2) and its focus at (4, 2).

A: The vertex of the parabola is the point of intersection parabola with its axis. The general form of…

Q: Find the vertex and focus of the parabola from the given equation and select its graph. ²+16y = 0

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Q: Find the standard form of the equation of the parabola. Vertex at the origin, focus at (0, 8)

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Q: Find a point on the parabola y - x* + 9 which is closest to the origin.

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Q: Find the vertex, focus, and directrix of the parabola x2 + 4x + 4y − 4 = 0, and sketch its graph.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: the parabola x^2-4x-4y=0

A: we have to find the vertex , focus and directrix of the given parabola. x2-4x-4y=0

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 vertex,focus,and directrix of the parabola given by y2 + 2y + 12x - 23 = 0.Then graph the…

A: y2+2y+12x-23=0⇒y2+2y=-12x+23⇒y2+2y+1=-12x+23+1⇒y+12=-12x+24⇒y--12=-12x-2 Now comparing with…

Q: What is the standard form of equation of a parabola with vertex at the origin and directrix x = 3? A…

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Q: Graph the parabola by finding the vertex, directrix, focus, and Latus Rectum. 4. y2-16y-12x +40 = 0…

A: we have to find the following

Q: Find the focus, the directrix, and the vertex of the parabola x^2 − x + 3y − 2 = 0

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Q: Find the vertex, focus, and directrix of the parabola y2 − 4y − 4x = 0, and sketch its graph.

A: Consider the equation of parabola, y2-4y-4x=0 Find the vertex, focus, and directrix of the parabola.…

Q: Find the coordinates of the points of intersection of the parabola y = x2 and y = x+3.

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Q: Determine the equation of the parabola vertex at (-4,-8) directrix is x=0.

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Q: What is the equation of the directrix of the parabola X+2x+4y-27=0 2

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Q: Find the standard form of the equation, focus, and directrix of the parabola. x2 +2x - 12y + 25 = 0

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Q: Find the point on the parabola * +y“ that is closest to the point (0, -3). =

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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: Solve for the directrix of the parabola y2 + 8x = 32

A: We have to solve for the directrix of the parabola y2 + 8x = 32.

Q: 2. Write the equation of the parabola x+ 6x+8y = 7 in standard form and identify the a) vertex, b)…

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

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Q: Find the vertex, focus and endpoints of the latus rectum of the parabola  4y^2 - x + 2 y = 0

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

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Q: Find the standard form of the equation of the parabola. Vertex at the origin, focus at (2, 0)

A: General equation of horizontal parabola is given by -y-k2 = 4px-h             ..........(1)where, h,…

Q: *.. .... Find the standard form of the equation of the parabola with the given characteristic(s) and…

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Q: Find the vertex, focus, and directrix of the parabola, and sketch its graph. x - 2x + 8y + 9-0…

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Q: Find the DE of parabolas with vertex and focus on the x-axis.

A: We know that equation of parabola when vertex and focus on the x-axis is, y2=4ax-h  where a and h…

Q: The directrix of the parabola x2 – 4 y = 0 is

A: According to our guidelines we are supposed to do only one question . Kindly repost the other…

Q: 1. Write the equation into the standard form of the equation of the parabola: -15 + 12x – 6y + y² =…

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

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Q: Find the vertex, focus, and directrix of the parabola y2 + 6y + 8x + 25 = 0, and sketch its graph.

A: Parabola:         y2+6y+8x+25=0=>y2+2.3y+9+8x+16=0=>(y+3)2=-8x-16=>-(y+3)28=x+2

Q: The focus of the parabola x2 =  8y is

A: I am going to find the focus of the parabola by comparing it with the standard form of parabola.

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 vertex Focus and divertrix to given the parabola x2 +6x+8y+25-0

A: The given equation is: x2+6x+8y+25=0 That can be written as…

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.