Suppose a and b are positive numbers. Sketch the parabolas y2 = 4a2 - 4ax      and         y2 = 4b2 + 4bx in the same diagram. Show that they intersect atand that each “a-parabola” is orthogonal to every “b-parabola".

Q: Give the property that defines all parabolas.

A: A parabola is a plane curve and it is mirror-symmetrical and approximately it can be in the shape of…

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

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Q: What is the length of the latus rectum (LR) of the parabola y = -÷(x – 2)“ + 5?

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Q: Determine the general equation of a parabola opening downwards whose vertex is at (3,-4) with a…

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Q: At what point does the line normal to the graph of y=5−4x+4x2 at (1,5) intersect the parabola a…

A: The given function is- y=5-4x+4x2.................1 Differentiating the above expression w.r.t. x-…

Q: Find an equation for parabola with vertex  (−1,3) and directrix x=−4.

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Q: What is the (unsigned) distance between the vertex and the focus of the parabola given by (x + 4)² =…

A: Given parabola equation,x + 42 = 19y + 5

Q: The vertex of a parabola is located at (−5, 6). If the parabola has a y-intercept of (0, 231), which…

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Q: Graph a hyperbola that opens in the x direction and is centered at at (-2, 1).

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Q: Suppose that point A(-2, -1) lies on a parabola with horizontal principal axis and whose vertex is…

A: Suppose that point A(-2, -1) lies on a parabola with horizontal principal axis and whose vertex is…

Q: In which direction does the parabola x = -y 2 + 3 open?

A: x=-y2+3 There are two patterns for a parabola, as it can be either vertical (opens up or down) or…

Q: A parabola with vertex (2, –3)and y-intercept (0, 5) can be expressed in vertex form as f(x) = (x –…

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

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Q: The vertical line passing through the vertex of a parabola is called the ......... .

A: Given The vertical line passing through the vertex of a parabola is called the ......... .

Q: . What is the snortest distance between the parabola y=2x² and the line y=4x-4

A: Shortest distance between two curves are always along the common normal.

Q: Any point on the parabola can be labeled (x, y), as shown. 4 3 2 (*, y) ¢ -6 -5 -4 -3 2 - 1 2 3 4 5…

A: According to figure equation of parabola in standered form X2=4bYnew equation of…

Q: Find the vertex of the given parabola. Give all values correct to 3 decimal places. y = 7x2 - 8x +…

A: A detailed solution is given below

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 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 equation of the parabola with vertex (−3,1)(−3,1) and yy-intercept 22(or (0,2)(0,2)).

A: topic - equation of a parabola

Q: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

A: Consider the given parabola y2=4ax Suppose Ax1 , y1  and  Bx2 , y2 be the ends of the focal chord of…

Q: The vertical line passing through the vertex of a parabola iscalled the_________

A: Solution:GivenThe vertical line passing through the vertex of a parabola is called the ...........

Q: Suppose that point A(-4,0) lies on a parabola whose focus is at (5,3). What is the length of the…

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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: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

A: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

Q: A parabola with a negative latus rectum has endpoints at (5, 1) and (5, -11) Where is the vertex? *

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Q: 13.2y – x = 4

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Q: Find the length of so-called semicubical parabola y = x3/2 on [5.2,9.6].

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Q: Find the point(s) of intersection of the parabola with equation y = x2 - 5x + 4 and the line with…

A: Given equations are,

Q: if the point (a, b) is on the parabola y=6x^2-(5785/12) that is closest to the point (0,4) than a ?

A: Given, y=6x2-578512 suppose x,y any point closest to 0,4  D=x-02+y-42 put y in equation,…

Q: Graph the two parabolas y = x2 and y = −x2 + 2x − 5 in the same coordinate plane. Find equations of…

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Q: Find the point on the parabola y=x^2 that is closest to the point (6,3) what is the distance between…

A: Given: To find the point on the parabola y=x2 that is closest to the point (6,3) what is the…

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: of the parabola. (to 3 places If he +

A: We have to find the following given conditions

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: Suppose a golf ball is driven so that it travels a distance of 200 feet as measured along the ground…

A: Given:A golf ball travels a distance of 200 feet as  measured along the ground and reaches an…

Q: List the roots of the parabola: y = x² + 2x + 5 In other words, list the solutions of the equation:…

A: The roots of a quadratics equation ax2+bx+c=0 is given by, x=-b±b2-4ac2a

Q: Correctly match up the vertex and axis of symmetry for this parabola.

A: We have to find the vertex and axis of symmetry according to the given information

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: Suppose that a point A(6,4) lies on a parabola whose focus is at (-1, 3). What is the length of its…

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Q: Assume the equation of a parabola and a line are given by y = x +2 x and y =3 x +6, respectively.…

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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: Show that,the area bounded by the parabola y^2 =4ax and a double ordinate is two third of the…

A: Let the parabola be y2=4ax Also let x =b be any double ordinate.Since the curve is symmetric about…

Q: Express your final answer in Mdx + Ndy = 0 1. Parabola whose vertex is at point P(13, 60).

A: The given data is: 1. Parabola whose vertex is at point P (13,60), Express your final answer in…

Q: Find the shortest distance of the point (10,4) to the parabola y=x2

A: Consider a  point on parabola  y=x2. Distance of this point with (10,4) s2=(x-10)2+(y-4)2…

Q: Suppose the axis of a parabola is parallel to the yy-axis and passing through the points (0,3),…

A: Given that, the axis of a parabola is parallel to the y-axis. Let the Vertex of the parabola (h, k)…

Q: Suppose a golf ball is driven so that it travels a distance of 200 feet as measured along the ground…

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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.