Find the equation for the parabola that has its focus at the (−394,−4) and has directrix at x=−25/4

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

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Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: find the equation for the parabola that has its vertex at the origin and has directrix at y = 1/44.

A: find the equation for the parabola that has its vertex at the origin and has directrix at y = 1/44.…

Q: Find the equation of the line tangent to the hyperbola x + 2xy - y + x = 5 at the point (3,7)

A: Given,            x2+2xy -y2+x =5 and point (3,7)

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: Find the angle at which the parabola y=x2−14 intersects the positive x−axis.

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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: Find the points on the curve x^2y = 2 nearest the origin.

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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: Find the value of Y for the hyperbola defined by the equation y² – x² = 7 at the point (3, 4). dx2

A: The equation is y2-x2=7. First find the value of dydx as follows.…

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

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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: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: Find the point on the hyperbola xy = 8 that is closest to the point (3,0)

A: Given: xy=8 so, y=8x now any point of given hyperbola can be written as x,8x so, let's that point on…

Q: Find the equation of the tangent to the hyperbola x2 - 4y2 = 9 at (5, 2).

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Q: Find a point on the parabola y - x* + 9 which is closest to the origin.

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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: Find the coordinates of the point on the parabola y = x² which is closest to the point (3, 0).

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Q: find the points on the parabola y=x^2 closest to the point (0,1)

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Q: Find the equation of the Hyperbola with asymptotes y=±2x and a vertex at (0, 10)

A: Given, The asymptotes of the hyperbola is  y=2x  and   y=-2x  and vertex at 0, 10 We have to find…

Q: 5. Find the equation of the hyperbola whose asymptotes are the straight lines x = 0 and y = 0 and…

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

A: Here we find the equation of parabola.

Q: Find the shorted distance from the point A(2, to a point on the parabola y = x². And find the point…

A: Let (x,y) = (x,x2) point on the parabola is closest to A Distance between (2 , 1/2) and (x,x2) is:…

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

A: Given- The parabola that has its vertex at the origin and satisfies the given condition(s).…

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: 2. Write the general equation of the parabola with directrix at x FG,-1), and v (. -1). 2

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Q: Find an equation of the hyperbola that has fodi at (-15,0) and (15, 0), and asymptotes y=x and y =

A: here we have to find the equation of hyperbola that has foci  at (-15,0) and (15,0) asymptotes…

Q: Find an equation for the parabola shown in the figure.

A: We have given Vertex: 1, 0 Focus:6, 0   The given graph is symmetric about x-axis. Equation of the…

Q: Find the equation for the parabola that has its vertex at the origin and has directrix at x=−1/28..

A: The standard form of equation of parabola with horizontal axis is given by the formula, y2=4px…

Q: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex…

A: Given

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: - 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: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: Fid the equation of the tanget to the parabola  x2 - 22x + 24y +169 = 0 at  the point whose focus…

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Q: Find the equations of the tangent and normal to the parabola y² - 2x - 4y -1 = 0 at the point (-2,1)

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Q: Find the point on the parabola x = t, y = t2, -∞ < t < ∞ closest to the point (2, 1/2).

A: Given Data The first equation is x=t. The second equation is y=t². The point is (2,1/2).…

Q: Find the length of the parabola given by c(t) = (t, t2) for 0 ≤ t ≤ 1.

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Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: The parabola y = Px² + Qx + R_passes through the coordinate (1,1) and has b. Determine the values of…

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Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

A: At the points of x-intercepts, y coordinates are 0, as along x-axis y=0.

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

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Q: The area of the region to the left of the parabola x=2y^2, to the right of the y-axis, and between…

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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 equation for the parabola that has its vertex at the origin and has directrix atI = 27…

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Q: Find an equation for the parabola that has its vertex at the origin and has a directric at x=1/29

A: We want to find out the equation of the parabola.

Q: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex…

A: Finding the equation of parabola

Q: Find the parabola with equation y = ax? + bx whose tangent line at (2, 8), is y = -2x + 12.

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Q: Find the points on the curve x2y = 2 nearest the origin.

A: The curve is x2y=2 Let x1,y1 and x2,y2 be two points, distance betwwen these points is x2-x12+y2-y12

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.