Find all hyperbolic lines that passes through i +1 and parallel to the y-axis.

Q: An ant is walking on the xy-plane is such a way that its distance to the point (2, 4) is always the…

A: Solution: Let the point P(x,y) is the position of Ant and given that the distance from P(x,y) to…

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 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 that an airplane main- tains a heading toward an airport at the origin. If vo = 500 mi/h and…

A: It is given that, an airplane maintains a heading toward an airport at origin, And, v0=500mi/h, w=50…

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: The end points of line segment 4, which lies in the xy-plane, are (-2, 5) and (6,-3). Which of the…

A: i have used the formula of midpoint of the two points and the slope point form of the straight line…

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: Draw the line y = 2.x + 1 and its image under reflection in the y-axis.

A: The given line is  y=2x+1 The slope of the line is 2, Y-intercept is 1,0 and X-intercept is -0.5,0.…

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 all points having a y-coordinate of - 3 whose distance from the point   (1, 2) is 13.

A: Consider the points are A = (x,-3) and B=(1,2) The distance between A and B is 13 units.   If the…

Q: Find the equation of the line in standard form (i.e., y = mx + b) that conatins the point (-3,5) and…

A: We have to find the equation of line in standard form if it is passing through the point -3, 5 and…

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

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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: Sketch a graph of the plane y = −2 and label any intercepts.

A: Given y = −2 .

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: 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,…

Q: Graph the parabola with a focus of ( – 2, 1), a directrix of y = 7, and goes through the point (4,…

A: We have to find the equation of parabola.

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

A: We have Vertex=(0,0)Directrix x=-15

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 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 the distance from the point (4, 3, 0) to the z-axis

A: To determine: Find the distance from the point (4, 3, 0) to the z-axis

Q: Find the following points of intersection. The point(s) of intersection of the parabola y = x2 + 2…

A: Given equation of parabola is y=x2+2 and equation of line is y=x+4. We have to find point of…

Q: Find the coordinates of the points of intersection of the parabola y = x2 and y = x+3.

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

A: Given query is to find the equation of the paraola.

Q: Write the equation of the straight line through (2, −3) with slope 3/4, in the parametric form r =…

A: Line passing through the point 2, -3 with slope 34.

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 the distance from the point (4, 3, 0) to the y-axis

A: We have to find the distance from the point 4, 3, 0 to the y-axis. We know that distance from the…

Q: Find the point on the surface fx,

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Q: Find the distance between the point (2, 9) and the line y = 3x + 4

A: Find the distance between the point (2, 9) and the line y = 3x + 4 To find the distance between a…

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: 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 a line containing the point (1, 7, -3) and parallel to the yz- plane.

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Q: 4. In general, if the line y is rotated 90° about (0, 0), explain how you can find the equation of…

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Q: What is the y-coordinate of all points in the xz-plane?

A: Plane: The y-coordinate of all points in the xz plane , i.e. we need to put y=0.

Q: Explain why a line in hyperbolic geometry must contain two distinct ideal points.

A: We have to answer given Questions.

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 distance from the point (-2, 1, 4) to the plane x = 3

A: Given: The point -2,1,4 and plane x=3 To find: Distance from the given point to the given plane.

Q: Graph the first-octant portion of each plane. 4x + 2y + 3z = 24

A: We have to find the graph the first-octant of the plane. To find x- intercept of the plane put 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)

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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Q: 33) Find the points of intersection between the line x - y - 2 = 0 and the parabola y = 4 - x 2.

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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.