Find the vertex and directrix of the parabola. y2+14y+ 4x +45= 0 vertex: directrix: step by step solution please

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

A: y2-4y-2x-4=0 On simplification, we get ⇒y2-4y=2x+4⇒y2-4y+4=2x+4+4⇒y-22=2x+8⇒y-22=2x+4⇒y-22=2x--4 Now…

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 focus, directrix, focal diameter, vertex and axis of symmetry for the parabola 23.12x=y^2

A: Given: The parabola is 23.12x=y2.   Calculation: Comparing with y2=4ax, we get 4a=23.12a=5.78…

Q: Convert the equation x2 - 2x - 4y + 9 = 0 to standard form by completing the square on x or y. Then…

A: Given:

Q: Find the focus, directrix, vertex and axis of symmetry for the parabola - 12(y + 2) = (x – 2)?. -

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Q: When graphed in the xyxy-plane, what is the yy-coordinate of the vertex of the parabola with…

A: given,       the parabola with equation y=−3(x−4)(x+6)

Q: Convert the equation x2 + 6x - 4y + 1 = 0 to standard form by completing the square on x or y. Then…

A: Convert the equation x2 + 6x - 4y + 1 = 0 to standard form by completing the square on x or y. Then…

Q: The equation of a parabola is y = -x 2 -4x + 3 . Give the equation of the axis of symmetry of the…

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Q: graph the parabola. determine the focus, vertex, and directrix  x2 = -12y  y2 = -14x  1/8 ( x -…

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Q: Convert the equation y2 - 2y + 12x - 35 = 0 to standard form by completing the square on x or y.…

A: Consider the provided parabola equation, y2-2y+12x-35=0 Find the vertex, focus, and directrix of the…

Q: Find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola - 13.32y = z

A: We are given the parabola : -13.32y=x2 ⇒x2=-13.32y--(1) On comparing with the equation of parabola ,…

Q: A straight line touches the rectangular hyperbola 9x² -9y² = 8 and the parabola y =32x. the equation…

A: Introduction :

Q: Convert the equation x2 + 8x - 4y + 8 = 0 to standard form by completing the square on x or y. Then…

A: We have the given equation as x2+8x-4y+8=0 Since y is not squared in this equation, we know that the…

Q: Find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola - 31.2x = y

A: The equation of a parabola y2=-31.2x Comparing with the standard equation y2=4ax4a=-31.2a=-7.8 Focus…

Q: The equation of a parabola is 12y = (x – 1)´ – 48 . Identify the vertex, focus, and directrix of the…

A: Parabola

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: Determine the vertex, focus, directrix, and axis of symmetry of the parabola with the equation y =…

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Q: Write the equation into the standard form of the equation of the parabola y² – 2y = 8x – 1. Locate…

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Q: 3. Find the coordinates of the vertex, focus, and the equation of axis of symmetry with equation y =…

A: Topic = Parabola  As per guidelines, At a time only one question can be answered out of different…

Q: Q1) Find an equation of the following parabola and sketch it where Vertex: (3,2) and Focus:(1,2)

A: Given the vertex 3,2 and the focus 1,2 of a parabola. We need to find the equation of the parabola…

Q: 2. Graph the parabola given by the equation, put it into standard form, and identify the vertex,…

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Q: Locate the vertex, focus, directrix and axis of symmetry of the parabola y^2-5x+12y=-16.

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Q: Find the equation of the parabola with the given properties Vertex (0,0), focus (5, 0). = x

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Q: The equation of a parabola is 12y=(x−1)2-48. Identify the vertex, focus, and directrix of the…

A: Topic:- geometry

Q: Find the equation of the axis of symmetry and the coordinates of the vertex of the parabola given by…

A: Given:

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: Graph the hyperbola by finding the center, vertices, and foci. Then use the b value to draw the box…

A: A hyperbola of the form (x-h)2a2-(y-k)2b2=1, then the transverse axis is parallel to the x-axis the…

Q: Find the equation of the axis of symmetry and the coordinates of the vertex of the parabola given by…

A: Given:

Q: Find the vertex, the focus, and the directrix of the parabola. x2 + 2x - 8y - 39 = 0

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Q: Can you assist me in answering this? (Not graded - solely for acquisitional purposes)

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Q: graph the parabola  and determine the focus, vertex and directrix  (3y - 6)2 = 36(x - 2)  x2 + 6x…

A: As we know that the the standard equation of the horizontal parabola is: y-k2=4px-h Where:  Vertex:…

Q: Find the vertex, focus, and directrix of the parabola with the given equation, y2 - 4x - 10y + 21 =…

A: first we will write it in the general form which is (y-h)2=4a(x-k) where (k, h) are the vertices…

Q: Which is the equation of the parabola with focus (0, 8) and directrix y = – 8?

A: We will use the fundamental property of parabola.

Q: Sketch and determine the opening, vertex and focus of the parabola with an equation of y? - 8x + 16…

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Q: Find the vertex, focus and directrix of the parabola: (y-7)2-6(x+9)

A: Given equation of the parabola is: (y - 7)^2 = 6 (x + 9) (y - 7)^2 = 4. (3/2), (x + 9) The above…

Q: Find the vertex and the axis of symmetry of the parabola given by the equation. y = −x2 + 8x − 18…

A: Provided equation of the parabola is given below.

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

A: Given equation, y2+2y+12x-23=0we have to find the vertex, focus and directrix of the given equation…

Q: Find the vertex, focus, and directrix of the parabola. y? – 4y – 2x - 4 = 0

A: The given parabola is  y2 - 4y - 2x - 4 = 0

Q: Use the equation x2 +18x – 2y -85 = 0 to determine the following for a parabola: a. equation in…

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Q: Find the equation of the axis of symmetry and the coordinates of the vertex of the parabola given by…

A: To determine the axis of symmetry and the vertex of the parabola.

Q: Find the standard equation of the hyperbola whose conjugate axis is on the directrix of the parabola…

A: Given: Conjugate axis of the hyperbola is on the directrix of the parabola The focus of the parabola…

Q: Q: Find the vertex, focus, and directrix of the parabola and sketch its graph, for the following…

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Q: Find the vertex, focus and directrix of the parabolas whose equations are as follows: y2 + 6y + 8x +…

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Q: Find the equation of the axis of symmetry of the following parabola algebraically. 3x2 + 6x - 12 y =…

A: The equation of the parabola y=3x2+6x-12. We have to find the equation of the axis of symmetry for…

Q: Given equation for parabola: 3x2+24x-12y=-108 a. What is the standard equation? (Express it in…

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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: By completing the square, find the standard form of the equation of the parabola: y = x^2 + 6x + 7…

A: y=x2+6x+7 On simplification, we get y=x2+6x+9-2⇒y=x+32-2

Q: (x – 4) = –12 (y + 3) - Find the vertex, focus, and directrix of the parabola.

A: The given equation is: x-42=-12y+3                                     (1)

Q: Find the equation of the axis of symmetry and the coordinates of the vertex of the parabola given by…

A: Given equation of the parabola is,x = y2 − 2y – 15

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.