The orthogonal trajectory of y= cex is a parabola of the form y = ax+b. Find the values of a & b so that the vertex is at (3,0).

Q: Find the coordinates of the vertex of the parabola y = x^2 - 4x + 1 using derivatives O (2, -3) O…

A: To find the vertex of the parabola by using derivatives

Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope −12 at x = −1, and…

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Q: Show that when a satellite is in elliptical orbit, its speed V is given by v² = k = k ( ² − ²) and…

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Q: Find the equations of both the tangent lines to the ellipse x^2 +3y^2 = 9 that passes through the…

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Q: 5) Find the shortest distance from the point P(3, 2,1) to the plane with 4. equation 2x + 3y – 2z =…

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Q: There is a parabola which has a minimum where the two lines 3x+6y-1=0 and 2x+ y-2=0 intersect. The…

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Q: Find a parabola with equation  y = ax2 + bx + c  that has slope  13  at x = 1, slope  −19  at x =…

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

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

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Q: In the xy-plane, a line that has the equation y = c for some constant c intersects a parabola at…

A: in the xy-plane a line that has the equation y=c for some constant c intersects a parabola at…

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: 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: Select a possible equation for a parabola with a vertex of (-1,3). Oy = (z + 1) (x – 3) | Oy = (z -…

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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: 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 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: Find a parabola with equation y= ax2 + bx +c that hasslope 4 at x=1  , slope -8 at x= -1 , and…

A: The parabola is y=ax2+bx+c. It has a slope of 4 at x=1 and slope of -8 at x=-1 and passes through…

Q: 1 Find the equation for the parabola that has its vertex at the origin and has directrix at y 27…

A: Given: y=-127.

Q: 8. Find a, b and c so that the parabola whose equation is y = ax² + bx + c has the vertex at (3,2)…

A: As we know that for the parabola y=ax2+bx+cthen its vertex is given by (-b2a,4ac-b24a)

Q: On a separate piece of paper, sketch the graph of the parabola y = x + 3. On the same graph, plot…

A: Given: Equation of parabola, y=x2+3

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: suppose that a non periodic comet will visit the solar system with the sun located at the focus of…

A: Parabolic trajectory of comet is 16y - 24 = x2. and sun located at its focus while earth at the…

Q: Find the point(s) on the parabola x =y closest to the point (0,3)

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Q: Show that the line b2xx1 - a2yy1 - a2b2 = 0 is tangent to the hyperbola b2x2 - a2y2 - a2b2 = 0 at…

A: Find dy/dx.Then find dy/dx at the point (x1,y1) by plugging x=x1 and y=y1

Q: 13. Find the point on the parabola y* = 2x that is nearest the point (1, 4). %3D

A: As per our guidelines we can solve only one question or three sub-parts. To ask more please…

Q: Determine the coordinates of points A and B on a parabola y midpoint of AB is as close as possible…

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Q: The orthogonal trajectory of y= Ce" is a parabola of the form y = ax+b. what is the value of b so…

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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: - Find a parabola with equation y = ax? + bx +c that has slope 4 at x = 1, slope –8 at x = -1, and…

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Q: 2. Determine the orthogonal trajectory of the family of hyperbolas y² – 121x² = c. c. Sketch some of…

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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: 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: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2. Ans: 2xy" -…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Ellipses

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Q: 1. Determine the orthogonal trajectories of the family of ellipses 16x? + 121y² = c. Sketch some of…

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Q: Find the equation of Parabola and Graph with the following information: Center at (0, 0) Vertices…

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Q: Find the maximum and minimum values of f(x, y) = 7x + y on the ellipse x2 + 9y² = 1

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Q: Find a parabola with equation y=ax^2+bx+c that has slope 4 at x = 1, slope -8 at x = -1, and passes…

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Q: It has been shown that when like particles with a common charge are hurled at each other, they…

A: Let's find.

Q: The graph of y^2 = x^3 is called a semicubical parabola. Determine the constant b so that the line y…

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Q: (a) Find and identify the traces of the quadratic surface x2 +y2 -z2 =1 and explain why the graph…

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Q: 1. Which of the following best describes the graph of y = x? – 4x + 2? a parabola with a vertex at…

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Q: Two parabolas are given: - C₁ is the curve of intersection between y = 1-2² and 2 = - C₂ is the…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 2. Which equation represents a parabola with vertex (4,4) and directrix y = 2? Oy=2x² - 4x + 4…

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Q: 1. Find the point on the parabola y = 3 – x² that is closest to the point (6, 0).

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Q: find the orthogonal trajectory of family of parabolas represented by the equation…

A: To find orthogonal trajectories of  y2=4ax.

Q: Find the shortest distance of the point (6,3) to the parabola y=x2

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Q: 19 Find the minimum value of the parabola y = x – 8x +

A: The minimum value of the parabola or any curve is obtained where y' = 0

Q: Find the equation of the line tangent to (a) The parabola z = 2x² - 3y², y = 1 at the point (-2,1,5)…

A: Given: we have to find equation of tangent lines   equation of tangent line : y-y1=m(x-x1)