Assume the equation of a parabola and a line are given by y = x +2 x and y =3 x +6, respectively. (a) Determine the intersection points between the parabola y x +2 x and the line y =3 x + 6.

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: Which of the following equations is the equation of tangent to the parabola y2 = 2x + 8 at point…

A: The given equation of parabola is: y2=2x+8

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: How can we find the slope of the parabola y?

A: You can’t find the slope of the parabola y , because a parabola is not a line. You can find the…

Q: Find the standard equation of the parabola with x intercepts at x = 2 and x -3, and a y-intercept at…

A: Solution is given below

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: Consider the parabola y = -x +4x + 9 and the line y=2x + 1. Solve for the x-coordinates at their…

A: x - coordinates of the point of intersection = ?

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: 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…

Q: How many common points does the parabola y=x2-2x-2 have with the straight line a) y=2x-6; b) x-…

A: Solving two equations

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 equation of the parabola with axis parallel to the x-axis, whose vertex is at (-1,7) and…

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Q: A parabola is given by the equation y = x^2 - 4x + 6. Find k so the line of equation y = 2x - k does…

A: We have to find the value of k for which the line intersect the parabola at two distinct points. To…

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 the equation of the line (in standard form , please) passing through the    Find the equation…

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Q: Find equations for two lines through the origin that are tangent to the ellipse a- 8x +y + 3 =0.

A: We are asked to find the equation of two lines that are tangent to the ellipse.

Q: Determine the relation of the ellipse x + 4y° = 32 and the line 2x +y-1 0.

A: To Determine: the relation between the ellipse x2+4y2=32 and the line 2x+y-1=0 Given: we have two…

Q: Find the equations of two lines through the origin that are tangent to the ellipse 2x - 6x+y +4 = 0

A: Consider the given equation:2x2−6x+y2+4=0Let a line y=mx+c is a tangent to the ellipse.Tangent…

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: 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: Determine the relation of the ellipse x + 4y = 32 and the line 2x +y-1 0.

A: Step:-1 Given conic and line is x2 +4y2 =32   and 2x+y-1=0 To find the relation between the ellipse…

Q: What is the equation of the line that contains the vertices of the hyperbola (x + 4)² (y + 2)² -1? 9…

A: Finding the vertices

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: Sketch the parabola and line on the same graph. y = 3x2 − 4  and  y = 2x + 4

A: point out zero of function and line and draw graph using these points

Q: 1. For the parabola equation: (y-2) = -3(x+4)^2 + 7, in which direction does the parabola open? *

A: We have to find the direction in which the given parabola opens.

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

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Q: 1. What is the equation of the line to the parabola y = x2 + 5x +1 through the 15 point at

A: Given, Parabola  y=x2+5x+1 Point 12, 154

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 is the equation of the directrix of the parabola X+2x+4y-27=0 2

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

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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: 2 What are the intersection points of the parabola given by the equation y = x“ – 9 and the line…

A: We are answering only the first question as per our honor code. Given, The equation of a parabola…

Q: The equation of the line touching both the parabolas y = 4x and x' =-32y is x-2y+1 = 0, then a is

A: Introduction :

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: Find equations for two lines through the origin that are tangent to the ellipse x - 8x + y² + 5 = 0.

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Q: ress 3x² + y² + 2z² + 6x – 4y

A: Given,            3x2+y2+2z2+6x-4y-12z+26=0

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

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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: Does the parabola y=2x^2-22x+3 have a tangent whose slope is -2? If so, find an equation for the…

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Q: How many common points does the parabola y=x2-2x-2 have with the straight line a) y=2x-6; b) x-2y=4?

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Q: 9. Find equations for two lines through the origin that are tangent to the ellipse 1² – 4x + 4y² =…

A: We have to find

Q: Match the parabola to an equation in standard form. 2+ -4 -2 4 6. Ta-1) -4- (x-1)2 = 4(y+1) (x+1)2 =…

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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)

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

A: