What is the length of the latus rectum of the parabola: y2 – 4y – 8x – 28 = 0?

Q: The parabola 8x² + 5y = 0, opens upward. downward. to the right. to the left.

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Q: What is the length of the latus rectum (LR) of the parabola y = -÷(x – 2)“ + 5?

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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: What is the standard form of the parabola, y + 2x + 10y + 9 = 0, given in conic form?

A: Do some rearrangement in the equation of given conic to convert it in standard form of equation

Q: Compute the length of the latus rectum of the parabola y2 + 8x – 6y + 25 = 0.

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Q: Show that the center of the osculating circle for the parabola y = x2 at the point (a, a2) is…

A: We need to show that the centre of the osculating circle for the parabola y = x2 at the point (a,…

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: Given a parabola's focus at (6, −4) and directrix at y = −7, how would you write its equation?

A: Equation of parabola: x-h2=4py-k Where vertex is (h, k) Focus is (h, k+p) And directrix y = k - p

Q: Identify the quadratic surface of the equation 6x? + 3y? + 222 + 24x – 6y – 12z + 39 = 0 Choose an…

A: Given, 6x ^ 2 + 3y ^ 2 + 2z ^ 2 + 24x - 6y - 12z + 39 = 0

Q: Where does the line x = 1 + 3t, y = 2−t intersect (a) the x-axis (b) the y-axis (c) the parabola y =…

A: Parametric equations are a set of equations where 2 or more variables are dependent on one single…

Q: 2=2X Find the point that is close' to the pont'(,4) on the parabola y

A: Explained below

Q: Cоmрute (x + y) dz, where is the portion of the parabola C y = 4 – x2 from -2 to 1+3i.

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Q: Find the quadratic surface and sketch the graph of r+y +- 4xyz = 1

A: The given equation is: x2+y2+z2-4xyz=1

Q: Determine the DE for: Parabolas with axis to the x- axis and with distance from focus to  vertex…

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Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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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: Given the general form of a parabola x2+6x-8y+10=0, what is the y coordinate the focus? (round to 3…

A: Explained below

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

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Q: What is the axis of symmetry of the parabola y=1/4x^2−14x+28?   A. y=28 B. x=7 C. x= -14 D. x=28

A: Given y=14x2-14x+28

Q: Show, by completing the square, that the parabolay = ax2 + bx +c can be obtained from y = ax 2 by a…

A: The given equation of parabola is y=ax2+bx+c. Rewrite the above equation as follows.…

Q: Show that the number 4p is the width of the parabola x2 = 4py (p>0) at the focus by showing that…

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Q: Find the evolute of the parabola y=x2.

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Q: 4x + y2 + 8y + 8 = 0   If it is a parabola, find the vertex, focus, and directrix.

A: As a first step we will convert the equation in the standard form of equation representing a…

Q: At what point does the normal to y = 3x – (5 + 4x) at (1, –6) intersect the parabola a second time?…

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Q: 4 SKetch the parabola and label the foces , ventees and dineder 2. 4 -6y -2utl=0

A: To find- Vertex, focus and directrix of a given parabola.

Q: How far from the x axis is the focus of the hyperbola (x^2)- (2y^2) + 4x + 4y+ 4 = 0?

A: the given equation of hyperbola is  x2- 2y2+4x+ 4y + 4 =0 it is asked to find how far is focus of…

Q: The parabola y = x² is shifted up by 4 unit %3D What is the equation of the new parabola?

A: Parabola:y=x2  shifted up by 4 units

Q: You have a parabolic bowl in the shape of the equationz=x^2+y^2, from z= 0 to z= 10. If you left the…

A: Let the parabolic bowl is filled till some height, h in..  So, the volume of the water in the bowl…

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

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Q: Find the vertex, focus and endpoints of the latus rectum of the parabola  4y^2 - x + 2 y = 0

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Q: Find the area of the ellipse given by x2/64+y2/ 4=1. Area =

A: Solution: The objective is to find the area of the ellipse given by x264+y24=1

Q: Determine the standard equation of the parabola opening upward, with focus at (0,6) and whose length…

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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: What is the equation of the parabola with a vertex at (4.8) and a directrix at y = 53

A: This is a simple question based on conic section (Topic is parabola) before attempting this question…

Q: 28. Find the directrix for the parabola. (y+ 3)2 + 8 2x x = 4 y = } 7/2

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Q: Evaluate x° ds where C is the part of the parabola y = x² from (0,0) to (2, 4).

A: Form the double integral and set the limits than integrate with respect to y and x.

Q: Find the DE of parabolas with vertex and focus on the x-axis.

A: We know that equation of parabola when vertex and focus on the x-axis is, y2=4ax-h  where a and h…

Q: Find the area of the largest rectangle that can be inscribed in the ellipse given by: x² + 4y? = 16

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Q: E. Express x^2– 12x + 16y – 60 = 0 to standard form and construct the parabola.

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Q: Evaluate y ds, where C is the parabola r (3t2, 3t), for 0 <t< 1. %3D

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Q: The directrix of the parabola x2 – 4 y = 0 is

A: According to our guidelines we are supposed to do only one question . Kindly repost the other…

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

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Q: For the parabola -2x 16y +4y2 + 13, for what value of y does r have a minimum?

A: This question is taken from the calculus in which we have to find the value of the y which makes the…

Q: Express your final answer in Mdx + Ndy = 0 1. Parabola whose vertex is at point P(13, 60).

A: The given data is: 1. Parabola whose vertex is at point P (13,60), Express your final answer in…

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

A: Vertices of parabolas = (0,0), Foci on the y-axis.

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: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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Q: Given x2 = 4py with p&gt; 0, the parabola opens (upward/downward/left/right).

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Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

A: Make equation of parabola