The parabola x2 = -4y is shifted left 1 unit and up 3 units to generate the parabola (x + 1)2 = -4(y - 3). a. Find the new parabola’s vertex, focus, and directrix. b. Plot the new vertex, focus, and directrix, and sketch in the parabola.

Q: The parabola y^2 = 8x is shifted down 2 units and right 1 unit to generate the parabola ( y + 2)^2 =…

A: (a) y2=8x ⇒4p=8⇒p=2 thus the directrix is x=-2, focus is (2,0) and vertex is (0,0).The new 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: 4. Classify the following as an ellipse, hyperbola, or parabola and sketch a graph like we have done…

A: a)The equation is, (9x2-36x)+(4y2-24y)=-36

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 equation for the parabola that has its vertex at the origin and has directrix at y = 7 The…

A: To find the equation of parabola that has tis vertex at the origin and has directrix at y=-17

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

A: The standard equation of open downward parabola having vertex at (h, k) and focus at length “p” from…

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

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Q: or the given equation of a parabola, determine the focus, vertex, and directrix. (x – 3)? = 32(y+ 4)…

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Q: Which of the following equations represents the parabola with vertex at (3, 2) and directrix y = 4?…

A: To find out the equation of the parabola.

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

A: Equation of parabola: x-h2=4py-k Where vertex is (h, k) Focus is (h, k+p) And directrix y = k - p

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

A: Given: Opens downward with focus 10 units away from the vertex.

Q: The parabola y=x^2+13 has it's focus at the point (b,c) where  b= c=

A: The given equation of the parabola is, y = x2+13. Also the parabola has its focus at (b, c).Consider…

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: 3. Write an equation for the parabola with focus (1, 3) and vertex (0, 3). a. y = 4(x – 3)² b. y =…

A: Given:      focus =1,3      vertex =0,3  The focus and vertex are horizontally aligned, so the…

Q: Given the general form of a parabola x2+6x-8y+10=0, what is the y coordinate the focus? (round to 3…

A: Explained below

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Q: Determine the two equations necessary to graph the hyperbola with a graphing calculator. y? - 64x? =…

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

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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…

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Q: Write the equation of the parabola with vertex at (-9, 0) and directrix at x = -10 a) + 9 1,2 49 b)…

A: Given

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

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Q: What is the focus of the following parabola? (y + 5)² = -12 (x - 2)

A: Given,  (y+5)2=-12(x-2)

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A: To find the equation of the standard form of parabola Focus -10,0 Directrix x=10

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Q: The equation of the directrix of a parabola is y = 5 and its focus is at (4,-7). What is the length…

A: given:Equation of direction of a parabola  is y=5focus 4,-7To calculate: length of latus rectum

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

A: The formula for a parabola in vertex form is:

Q: Graph the parabola. y=x y3x+10x+21 Plot five points on the parabola: the vertex, two points to the…

A: See the details solution in below

Q: Identify a and b for the hyperbola with equation a2 y? 1. 62 - a = b = %D

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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: nd the equation of the parabola with vertex at (5,-2) and focus at (5,-4). (x – 5)² = 8(y + 2) (x +…

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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: The Focus and the Directrix of the parabola (x – 8)² = 8(y – 3) are -

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Q: Which equation represents a parabola with focus (2, 6) and directrix y = 2? A. y+4=(x-2)² 10 B.…

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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 the equation of the parabola with focus at (3,5) and directrix y = 3.

A: First I have written a formula of parabola with given focus and directrix, just use the formula for…

Q: Which of the following is the equation of a parabola with a vertex (−2,3) and directrix y=7?

A: Given, Vertex: (-2,3) Directrix: y=7 To find: The equation of the parabola.

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

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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: Write the equation of a parabola whose directrix is y = 7.5 and has a focus at ( – 4, – 4.5). -

A: The equation of parabola whose directrix is y=-7.5 and has a focus at (-4,-4.5).

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus : (0,…

A: Given : Direction : y = 25 Focus : ( 0 , -25 ) Vertex is exactly between Directrix and Focus

Q: given the directrix of y = 6 and focus of (0,40, which is the equation of the parabola?

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Q: Write the equation for a parabola with a focus at (-6,0) and a directix at x=-2

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

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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)