Find the equation of the evolute of the parabola y? = 12x.

Q: Give the standard equation of the parabola with focus (-3,0) and directrix x=3

A: Standard equation of parabola is y2=±4ax Given that focus of parabola is (-3,0) and directrix is…

Q: Write the equation of the hyperbola 36x? – 25y? + 288x – 150y – 549 = 0 in standard form (x – h)?…

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Q: What is the nearest distance from the point P(6,0) to the parabola? y^2=8x

A: GivenP(6.0)y2=8x To find nearest distance

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

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Q: Write the equation of the hyperbola 4x2 – 25y? + 8x + 250y – 721 = 0 in standard form (x – h)? (y –…

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Q: Write the equation of the parabola given by y? + 2y + 12x – 23 = 0 in standard form. %3D -

A: Given equation of parabola is y2 + 2y + 12x - 23 = 0

Q: Write the equation of the hyperbola centered at the origin, with length of the horizontal transverse…

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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: Write the equation of the hyperbola centered at the origin, with length of the horizontal transverse…

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Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 3. (two…

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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: Write the equation of a hyperbola with center at the origin, passing though (±4,0) with no…

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Q: What is the measure of the focal width of the parabola y+2y+4x-3=0 ?

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Q: What is the y-intercept of the following parabola?

A: The question is taken from the parabola in which we have to find the y-intercept of the given…

Q: given the equation of parabola y^2 -8x -4y -20=0,find the length of latus rectum

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Q: Find the equation of the directrix of the parabola y=16x.

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Q: y=2x + 8x +9 Plot five points on the parabola: the vertex, two points to the left of the vertex, and…

A: Equation of parabola in standard form is  y = ax²+bx+c

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

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Q: find the equation of the parabola y = ax? + bx + c that passes through the points. (0, 3), (1, 4),…

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Q: What is the equation of the directrix of the parabola x2 + 2x+4y– 27=0? A y=8 B y=0 (© y= -2 D y=6

A: Solution ) x2 + 2x + 4y - 27 = 0 Add 1 and subtract 1 in equation  x2 + 2x +1  - 1  + 4y - 27 = 0…

Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 3.

A: Given :          The equation of directrix of the parabola is x + 1 = 0          The length of the…

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: Find the evolute of the parabola y=x2.

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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: Sketch the parabola and line on the same graph. y = x + 4 and y = 2x + 2 %D

A: Consider the given parabola y=x2+4 and the line y=2x+2. Use online graphing calculator and sketch…

Q: b) Determine the concavity, Y-Intercept, X- intercept of the quadratic equation And sketch the…

A: Clearly shows the turning poin of the quadratic equation is (10, -50)

Q: (b) Find the evolute of the parabola y? = 4ax.

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Q: Write the equation into the standard for -4.x? + y? – 16x – 2y – 19 = 0. Locate hyperbola

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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: Write the equation of the hyperbola centered at the origin, with length of the horizontal transverse…

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

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Q: determine the coordinates of the y intercept of the parabola.

A: To determine the coordinates of the y intercept of the parabola.

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

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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: Solve for the directrix of the parabola y2 + 8x = 32

A: We have to solve for the directrix of the parabola y2 + 8x = 32.

Q: Find the point on the parabola y 2 =2x that is closest to the  point ( 1, 4)

A: Given: y2=2x let's point on parabola is t22,t now, if point1,4 is closest to t22,t2 then product of…

Q: Find an equation of the parabola with focus (-8,5) and directnx X = 4,

A: Parabola is the locus of a point, which moves so that its distance from a point called focus and a…

Q: Write the equation of a parabola whose directrix is y = 7.5 and has a focus at ( – 4, – 4.5). -

A: The equation of parabola whose directrix is y=-7.5 and has a focus at (-4,-4.5).

Q: Describe the part of a hyperbola given by the equation.

A: Given: y=94x2-16

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

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Q: Write the equation of the hyperbola 9x² – 4y? – 54x + 32y – 19 = 0 in standard form (x – h)? (y –…

A: Write the equation of the hyperbola  9x2 - 4y2 -54x +32 y  -19 =0 In the standard form  (x-h)2 /a2 -…

Q: Consider the parabola given by the equation: 1æ? y = 2x + 8 -

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Q: Write the equation of a parabola whose directrix is y = 10.75 and has a focus at (-3, 1.25).

A: Given :focus -3, 1.25

Q: Describe how the parabolas y = x2 + bx change as b changes from -oo to oo.

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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: Write the equation of the parabola in the form y = a(x- h) + kor x = a(y - k) +h'

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Q: Calculate y′′ for the parabola equation y2=4x.

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Q: Determine the standard equation of parabola Show your solutions X²+2y+y-1=0

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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.