5) Find the vertex and axis of symmetry of the parabola with focus F(7/2,3) and directrix line x=1/2. * Vertex (2,3); Axis of symmetry, y=-3 O Vertex (-2,-3); Axis of symmetry, y=2 O Vertex (2,3); Axis of symmetry, y=3 O Vertex (2,3); Axis of symmetry, y=2

Q: Given the focus and directrix of a parabola, identify its important characteristics. 10 8 -10 -8 -6…

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Q: A flashlight is shaped like a paraboloid and the light source is placed at the focus so that the…

A: Given the flashlight is shaped like a paraboloid and the light source is placed at the focus so that…

Q: 7) Determine the shape of the I point parabola with focus F(2,5/2) and directrix line y=7/2. *

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Q: Given the focus and directrix of a parabola, identify its important characteristics. 10 8 -10 -8 -6…

A:

Q: What is the length of the latus rectum of a parabola having its vertex at the origin and focus at…

A: The length of latus rectum of parabola = 4a

Q: A parabola of y=x^2 has been regraphed and now sits with each side plotted at (-3,5) and (3,5) and…

A:

Q: 3. Determine the orthogonal trajectory of the family of parabolas x² – y + 32x = 0. %3D Sketch some…

A:

Q: "What is the families of the curve of all Parabolas with axis parallel to the x-axis

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Q: What is the family of curves for all parabolas with axes parallel to the y-axis.

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Q: 5 Find an equation of the hyperbola having foci at (-2, - 3-/29) and (-2, – 3+ /29) and asymptotes…

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Q: The orthogonal trajectory of y=cex is a parabola of the form y2=ax+b. Find the values of a and b so…

A: See the details solution in below

Q: How to write the equation of a hyperbola  Foci at (-10,0)(10,0); asymptote the line y=-x

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

A: Given:Vertex=0,0Directrix y=-3Equation of parabola:x-h2=4py-k

Q: Find the standard form of the equation of the parabola with the given characteristics. vertex: (2,4)…

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Q: Activity 2 Classify the graph of the equation as circle, a parabola, an ellipse, or a hyper Show…

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Q: 17. If the focus of the parabola is (-2, 1) and the directrix has the equation x + y = 3 then the…

A: Given Focus of parabola f (-2, 1) Equation of directrix is x+y =3   Here the objective is to find…

Q: The hyperbola with asymptotes having the equations y -x and y--x and one verlex at (2, 0) has the…

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Q: By differentiating implicitly, find the slope of the hyperboloid x² + y? - z2 = 1 in the x-direction…

A:

Q: A parabola has its axis parallel to the x-axis, one end of its latus rectum at (-15/4,3/2) and…

A: Given Information:A parabola has axis parallel to the x-axis.Latus rectum at -154 , 32Vertex at (-1,…

Q: Find an equation for the parabola with vertex V(0, 0) and Focus F(0, 2), and sketch its graph.

A: We have given vertex V0,0 and focus F0,2. Given the vertex of the parabola is V0,0 and focus is at…

Q: 17. Parabolas with axis parallel to the x-axis and with distance from vertex to focus fixed as a. Am…

A: This question is about family of parabolas.

Q: (result of elimination of constant) * Parabola with vertex and focus on the y-axis

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Q: Find the minimum distance from the point (4,2) to the parabola y2 = 8x.

A: We have to find the minimum distance from the point (4,2) to the parabola y2=8x.

Q: The parabola passes through the points (−3/2, – 1), (1, 5) and vertex is at (0, 4) with a horizontal…

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Q: Find the points of intersection between the parabolas y = 6 - x 2 and y = x 2 - 2. %3D

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

A: We have Vertex=(0,0)Directrix x=-15

Q: Find the standard equation of the hyperbola 1. Asymptotes y=4/3x + 1/3 and y=-4/3x +41/3, a vertex…

A: Solution of the problem as follows

Q: 8. The equation of parabola with vertex (0,0), passing through (-2,8) and axis that coincides with…

A: Problem number 8 is solved. Solving more than one question is against the policy of bartleby.

Q: Sketch the parabola y = x² + 2x +1. Use arrows to indicate the maximum and minimum values of y over…

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Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 3. (two…

A: The equation of directrix of the parabola is x+1=0. The length of the latus rectum is 3. The…

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

A: Here we find the equation of parabola.

Q: Sketch parabola y = x2 – 10x + 16 by plotting a few points to left and right of the vertex. (Find…

A: Given parabola y=x2-10x+16                  ....(1)

Q: 3. Find an equation of the hyperbola having foci at (4, 3-V 52) and (4, 3 +/52) and asymptotes at y=…

A: Focii: (4, 3+52) & (4, 3-52)Assymptotes : y=3x2-3 , y=-3x2+9Let vertex by represented by (h,k)…

Q: b. Family of parabolas whose vertex is along the line y -2, %3D

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Q: Find the standard form equation for a hyperbola with vertices at (0, 3) and (0, – 3) and asymptote y…

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Q: Find the minimum distance between the point (5,1) and the parabola y=-x2 ?.

A: Find the minimum distance between the point (5, 1) and the parabola y = -x2?

Q: What is the minimum vertical distance between the parabola y =x2 +1and y =x -x2 ?

A: Given:

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

A: equation of parabola  (x - h)2 = 4p (y - k) where (h,k)=(0,0) vertex ordinates directrix y=3 , y= k…

Q: 1. Determine the equation of the parabola whose vertex is at the point (-1, –1) and whose directrix…

A: We have to determine the equation of the parabola whose vertex is at the point (-1,-1) and whose…

Q: What point on the parabola y = 3- x² is closest to the point (3,3)? The point on the parabola y = 3…

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Q: Find the equation of a parabola that has a vertex of (2, -4) and contains the point (1, -7).…

A: Given  Vertex of parabola (2,-4)  And contains the points (1,-7)

Q: 10. focus of parabola X-12y is 1- (6,0)

A: Here we have to find the focus of the parabola,  The given parabola is X2=12y .............. (1)

Q: 1. Sketch the graph for a parabola with AOS at x = -3, minimum of 2, and an y-intercept at 5. Label…

A: We are authorized to answer one question at a time, since you have not me mentioned which question…

Q: 9. Find an equation of the parabola that satisfies the given condition: Vertex V(-1,0) and focus…

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Q: What point on the parabola y = 1-x is closest to the point (1,1)? The point on the parabola y = 1-x2…

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Q: 4. What is the family of curves for all parabolas with axes parallel to the y-axis. Add File

A: We will find out the required solution.

Q: Find the standard form equation for a hyperbola with vertices at (8, 0) and ( – 8, 0) and asymptote…

A: The standard form of the equation of a hyperbola with center (0,0) and transverse axis on the x-axis…

Q: 8. The equation of parabola with vertex (0,0), passing through (-2,8) and axis that coincides with…

A: Note:-  In the given questions No. 7 is incomplete because in this option(a) is missing + and -…

Q: 2. Graph an ellipse with center at (1,2), vertices at (6,2)and (-4, 2), co-vertices at (1, 6)and (1,…

A: Given:        Center at 1,2        Vertices at 6,2 and -4,2         co-vertices at 1,6 and 1,-2…

Q: 33) Find the points of intersection between the line x - y - 2 = 0 and the parabola y = 4 - x 2.

A:

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.