List the roots of the parabola: y = x² + 2x + 5 In other words, list the solutions of the equation: 0 = x + 2x +5 %3D • Your answers must be in exact form, do not give their decimal values. • Separate multiple roots with a comma.

Q: Find the standard equation of the parabola with directrix x + 1 = 0, axis y = 1 and the length of…

A: If the axis of parabola is y = 1, then the parabola is horizontal. As we know that the standard…

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: 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: The x-axis and the y-axis are asymptotes of the equilateral hyperbola whose equation is xy = 9. Find…

A: Given: xy=9 we know that length of transverse axis and conjugate axis is equal for rectangular…

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

A: Given equation is  x=23y2-36

Q: Find the equation of the hyperbola with center (o, o), a vertex at (5, o) and an extremity at (o,…

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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: Examine this parabola and determine the solutions.

A: given parabola :

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: Find the equation of parabola given these three points using quadratic formula. (1,27) (18,45)…

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Q: solve for the focus of the parabola 8y = -x2 + 4x + 36

A: Solution:-     As we know,           The equation of a parabola in a vertex form is…

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

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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: A cable suspended between two posts that are of the same height and 20 meters apart has a sag of 1/2…

A: Given: A cable suspended between two posts that are of the same height and 20 meters apart has a…

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: If the diameter of the parabolic mirror is 100 meters and the sunlight is focused 25 meters from the…

A: It is given that the diameter of the parabolic dish is 100 m and the focus of the dish is 25 m.

Q: If the axis of symmetry of a parabola is given by x = 4, is it possible for the directrix to have…

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Q: Use the given information to write the equation of the parabola.

A: Since the directrix is y=3, So then the foci will be (0,-3).   Find equation of parabola on y- axis:…

Q: Find the standard equation of the parabola with directrix x + 1 = 0, axis y = 1 and the length of…

A: Find the standard equation of the parabola with directrix x + 1 = 0, axis y = 1 and the length of…

Q: The parabola y2 =-14x has it's focus at the point (b,0) where b is?

A: The standard equation of parabola for this condition is y2=-4ax here  Focus (-a, 0)   Now, we have…

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 of the parabola with directrix y = 3, axis x = 0, and latus rectum 4. (two answers…

A: The standard equation of the parabola is (y-k)=4a(x-h)2, where h and k are the coordinates of the…

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

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Q: Given the general form of a parabola x2+8x-12y+11=0, what is the equation of the directrix? y=_____.…

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Q: Find an equation of the parabola (in general form) given the following condition: opens upward,…

A: Formula for equation of parabola open upwards is: (x-h)2=4a(y-k) ......(1) Where (h,k) is vertex

Q: The parabola y = x² is shifted up by 7 units and to the left by 1 unit. What is the equation of the…

A: Equation of parabola is given as y=x2. If the parabola is shifted by a units and to the left by b…

Q: solve for the equation in standard form then graph -Parabola with ?+1=0 as the directrix, ?=1 as…

A: To solve the given equation in standard  form and then plot the graph.

Q: if the point (a, b) is on the parabola y=6x^2-(5785/12) that is closest to the point (0,4) than a ?

A: Given, y=6x2-578512 suppose x,y any point closest to 0,4  D=x-02+y-42 put y in equation,…

Q: Find the directrix of the parabola described by the equation 6 (x – 3) + (y + 2)? = 0 O x = } O x =…

A: The  parabola with vertex at (h,k) and focus at (h-a,k) has a standard equation, (y-k)2=-4a(x-h) The…

Q: An engineer is designing a flashlight using a parabolic reflecting mirror and a light source.  The…

A: Desining a flashlight: Position the parabola with its vertex at the origin and opening upward.…

Q: What are the coordinates of the end points of the latus rectum of the parabola with equation a - 2z…

A: What are the coordinates of the end points of the latus rectum of the parabola with equation…

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

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

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Q: Determine the equation of the parabola given:

A: Graph of the hyperbola is given, we have to find its equation

Q: the center-radius of the equationn 9x²-18 x+ 9+9y? + 12y=12 be obtained by adding both sides of 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: 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 an equation of the paranola in standard form: with the vertex at V (2,-4) and directrix y= -5

A: Find an equation of the parabola in standard form: with the vertex at V (2,-4) and directrix y= -5

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

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Q: How many derivations are required for the problem involving parabolas with axis parallel to the…

A: Since you have asked multiple questions, we will solve first one for you. If you want other question…

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 of the parabola with directrix y = 3, axis x = 0, and latus rectum 4

A: Given: Equation of directrix:y=3……1Equation of axis:x=0……2Length of latus rectum:4……3

Q: Find the equation of the parabola with directrix x + 2 = 0, axis y = 4, and latus rectum 4.

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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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