The graph of y² = x³ is called a semicubical parabola and is shown in the accompanying figure. Determine the constant b so that the line y = -x + b meets this graph orthogonally. y? = x y = -* +

Q: Find the parabola with equation y=x^2+bx+c that has slope of 8 when x=9 and passes through the…

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

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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: Suppose a and b are positive numbers. Sketch the parabolas y2 = 4a2 - 4ax      and         y2 = 4b2…

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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: Sketch a graph of the plane 3x + 6y + 2z = 6 and label any intercepts.

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

A: equation of parabola:-

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: Find the equation of parabola “y = ax2 + bx + c” passing through points (1, -6), (2, -3), (-1, 0)

A: Consider the given points and the equation of the parabola. Obtain the system of equations with a, b…

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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: Find the equation of the parabola and put it in the form f(x)= ax^2 +bx+c  Given:  vertex: (7, -4)…

A: Explained below

Q: Find the equation for the plane through the points Po(-2,3,5), Qo(-4, – 1, - 2), and Ro(4,1,0).

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Q: Find an equation of a plane passing through the points (1, –3, –59), (–3, 2, 54) and perpendicular…

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Q: What is the equation of a parabola that intersects the x-axis at points (-1, 0) and (3, 0)?   A. y…

A: Given that: A parabola intersects x-axis at (-1, 0) and (3, 0)

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: 17. Explain why it is not possible for a line in three-space to be represented by a scalar equation…

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Q: The point (1,2) lies on the parabola: y 3x2 -2x+2 %3D

A: Thanks for the question :)And your upvote will be really appreciable ;) False statement (1,2) does…

Q: Find the equation of the plane perpendicular to the y-axis and passing through the point (3,2,-2)

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Q: Consider a parabola that intersects the x-axis at points (-1, 0) and (3, 0).

A: We need to find an equation of parabola that intersects the x-axis at (-1, 0) and (3, 0). Thus,…

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A: Here we have to find the equation of a plane that passes through the point (0,0,0) and contains the…

Q: A parabola has an equation of y² = 4x. Find the nearest distance from the point (-3, 6) to the %3D…

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Q: Find an equation of the plane that contains all the points that are equidistant from the given…

A: Let the point P(x,y,z) be on the required plane which is equidistant from the given points (1, 0, 2)…

Q: Sketch a graph of the plane 2x − y + 3z = 4 and label any intercepts.

A: To find the x-intercept for ax+by+cz=p, let y and z equal 0 and solve for x. find the y and z…

Q: Find the shortest distance between the point A(2, 5, –7) and the plane 3x – 5y + 6z = 9.

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the equation of a parabola that has a vertex of (-2, -1) and contains the point (0, 3).…

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Q: Find the point at which the line (-4, 1,1) + t(2, -5, 4) intersects the plane -5x+ 3y – 3z = -54.

A: the given line is  xyz=-411+t2-54 xyz=-411+2t-5t4t xyz=-4+2t1-5t1+4t

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: 4 - Find an equation of the Planc perpendicular to each of the planes X-y +2=0 and 2x ty - 4z -5 =0…

A: A detailed solution is given below

Q: (3) Find the coordinates of the points of intersection of the parabola y = x2 - ax and the line y =…

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Q: Find the linear equation of the plane through the point (0, 1, 1), (1, 0, 1), and (1, 1, O)

A: Consider the point (0,1,1). Take option (a) x-y-z+2=0-1-1+2=0 Take option (b) -x+y-z+2=-0+1-1+2=2≠0…

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: Find the coordinates of the intersection point of the lines x_1 + 3x_2 = 3 and −2x_1 + 4x_2 = 1 in…

A: Solved below

Q: Find the point at which the line (-3, -4,-2)+t(5, -4,-2) intersects the plane -5x +3y+z= -155.

A: Given: line equation: -3,-4,-2 +t (5,-4,-2) Then equation of line from parametric equation is given…

Q: Find an equation of the plane that contains all the points that are equidistant from the given…

A: Let plane contain point x,y,z.

Q: Find the equation of the plane containing the x-axis and passing through the point (4,3,1/5)

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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: 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 an equation of the plane that passes through the point (18, -16, 9) and contains the line given…

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Q: Sketch a graph of the plane 4x + 2y + 6z = 12 and label any intercepts.

A: Given equation is: 4x + 2y + 6z = 12

Q: Find the point P on the parabola y = x2 closest to the point (57, 0). (х, у) %3D ]-«

A: Given the equation of parabolay=x2         ........(1)

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

A: Solution is here