Sketch parabola y = x2 – 10x + 16 by plotting a few points to left and right of the vertex. (Find vertex using Vx = -b/2a)

Q: Find the standard equation of the hyperbola. Two corners of auxiliary rectangle at (−4 ,−7) and (0…

A: Given: The two corners of the auxiliary rectangle of a hyperbola are at -4,-7 and 0,0 and transverse…

Q: Finally, determine a. The parabola passes through the point (0, 5). Substitute the values of x and y…

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Q: 9. Sketch the parabola y =-x +8x-12, show all the intercepts, the axis symmetry and the vertex

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

A: equation of parabola:-

Q: Find the equation of the parabola with vertex (2, 4) and directrix x = –3

A: Given: Vertex (2,4)

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 an equation of the parabola with vertex (5,-5) and directrix y=-3   .

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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 the general equation of the parabola with vertex at the origin and focus at (-4, 0)

A: The general equation of a parabola with vertex (h,k) is (y-k)2=4a(x-h)

Q: Determine the DE for: Parabolas with axis to the x- axis and with distance from focus to  vertex…

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Q: Find the least and greatest distances from the origin to a point on the ellipse x²+4y²=16.

A: Topic:- geometry

Q: Find the standard form of the equation of the parabola with the given characteristics Vertex: (0, 5)…

A: Given vertex and directrix are (0, 5) and y= -3. The equation of parabola is x-h2=4py-k where (h, k)…

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

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: What is the equation of the directrix of the parabola having a vertex at (6,0), passing through…

A: Given:- What is the equation of the directrix of the parabola having a vertex at (6,0), passing…

Q: Find the equation for the parabola that has its vertex at the 1 origin and has directrix at y 41…

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Q: Find b and c so that the parabola with equation y = 4x2 - bx - c has a vertex at (2 , 4)?

A: Using the vertex formula we find the x value of the vertex[formula: x value of vertex of Ax^2+Bx+C=0…

Q: Give 3 points that lie on the parabola y=x^2-5x-2

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Q: Find the standard equation of the parabola with directrix x + 1 = 0, axis y = 1 and the length of…

A: Find the standard equation of the parabola with directrix x + 1 = 0, axis y = 1 and the length of…

Q: Sketch the parabola and line on the same graph. y = x2 + 5  and  y = 2x + 1

A: The equation of curves are  y = x2 + 5  and  y = 2x + 1

Q: The parabola y2 =-14x has it's focus at the point (b,0) where b is?

A: The standard equation of parabola for this condition is y2=-4ax here  Focus (-a, 0)   Now, we have…

Q: find the equation of the parabola with the given properties. Vertex (0, 0), directrix y = −5

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Q: Explain how to use y2 = 8x to find the parabola’s focus and directrix.

A: Given: y2=8x   To find: The parabola’s focus and directrix

Q: Find an equation of the parabola with vertex (3, 4) and directrix y = 1.

A: Graph of parabola :

Q: what is the equation of a parabola with a vertex at (4, 8) and a directrix at y=5

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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 the point on the parabola y = x³ that is closest to the point (1, 2) with two digits accuracy…

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Q: Find an equation of the parabola with vertex (−4, −2) and directrix y=−7.

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Q: Find equations for the osculating circles of the parabola y=0.5x2 at the points (0,0) and (-1,1/2).

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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: Find an equation for the hyperbola that satisfies the Vertices: (±1, 0), asymptotes: y = ±3x

A: Given,        Vertices: (±1, 0)    asymptotes: y=±3x

Q: What are the coordinates of the end points of the latus rectum of the parabola with equation a - 2z…

A: What are the coordinates of the end points of the latus rectum of the parabola with equation…

Q: Determine the points of intersection of the parabola y=2x^2 +12x +10 and the line y=4x+2

A: I am attaching image so that you understand each and every step.

Q: Find an equation of the hyperbola that has foci at (-10,0) and (10,0) , and asymptotes y=3x and…

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Q: Sketch the parabola and line on the same graph. y = x2 + 4 and y = 2x + 2

A: Given, y=x2+4   y=2x+2  The graph of given functions can be plotted as shown in the figure below.

Q: 15. 20y - 3 - 40y + 12x = 52

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Q: Find the points on the ellipse  3x2 + y2 = 3  that are farthest away from the point (−1, 0).

A: Given 3x2+y2=3

Q: Find the points of intersection of the parabola with equation 2x + y² + 4y – 2 = 0 and the line…

A: Here we find the intersecting point of parabola and the line.

Q: What is the equation of the parabola with a vertex at (4.8) and a directrix at y = 53

A: This is a simple question based on conic section (Topic is parabola) before attempting this question…

Q: Find an equation of the parabola with vertex (5, – 1) and directrix y = -4.

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Q: Find the points on the ellipse 5x2 + y² = 5 that are farthest away from the point (1, 0). smaller…

A: To find the points on the ellipse 5x2+y2=5, that are farthest away from the point 1, 0.

Q: Find the equation of the parabola that is symmetric about y axis with vertex at the origin and…

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Q: Find an equation of the paranola in standard form: with the vertex at V (2,-4) and directrix y= -5

A: Find an equation of the parabola in standard form: with the vertex at V (2,-4) and directrix y= -5

Q: Find the equation for the hyperbola that asymptottes (y - 3) = +- 1/square root of 2 * (x+3) and…

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Q: Find an equation of the parabola with vertex (4,2) and directrix x=-1

A: Find the equation of parabola:

Q: Find the point(s) on the ellipse 4x² + y² = 4 that are farthest from the point (1,0).

A: We need to find the points on the ellipse that is farthest from the given point. According to first…

Q: Determine the coefficients a, b, and c of the parabola y = ax² + bx +c that passes through the point…

A: Solution is here

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.