It is true that the vertex is halfway between tje focus and the directrix on the principal axis

Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 1) and directrix…

A: Given that Focus of parabola is F0, 1. Directrix is y=-1. We have to prove that y=14x2 is the…

Q: The focus of the parabola y^2 = 4x is at

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Q: What is the (unsigned) distance between the vertex and the focus of the parabola given by (x + 4)² =…

A: Given parabola equation,x + 42 = 19y + 5

Q: Find the equation of the parabola with vertex at the origin and satisfies the condition: Focus…

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Q: What is the distance between the vertices of the hyperbola with one focus at (-1, 4) and co-vertices…

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Q: at

A: Given focus (-5,7) Directrix x=1

Q: Find the standard equation of the parabola which satisfies the given condition. Focus (7, 11),…

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Q: For a hyperbola, the foci lie on a line called the_________

A: Given that, A statement, " For a hyperbola, the foci lie on a line called the ______ ."

Q: A flashlight is shaped like a paraboloid and the light source is placed at the focus so that the…

A: Given the flashlight is shaped like a paraboloid and the light source is placed at the focus so that…

Q: Identify the quadric surface and sketch the graph. z = x2 + 4y2

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Q: Explain why the dots in the Figure given below lie on a parabola. Where are the focus and directrix…

A: the figure in the diagram is a circle so It should be in the form of x2+y2=K Now y =c or some…

Q: Given a focus of (2, 4) and a directrix of y= -2, find the equation for the parabola. (2-

A: Given:    focus (2 , 4)    directrix y = -2

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: suppose that the bulb of a flashlight is placed at the focus of its parabolic reflector. if the…

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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: Use the Distance Formula to show that the equation of the parabola with focus F(0, 2) and directrix…

A: Given:            Focus of parabola is : F(0,2)Directrix is:​y=−2.

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

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Q: The line perpendicular to the directrix and passing through the focus of a parabola is called the…

A: Given:

Q: 5. Identify the focus of the parabola given by y = 8x². O (0,) O (-8,0) O (0,0) O (8)

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Q: Find the Parabola with Focus (7,-2) and Directrix x=-9

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Q: The figure on the right shows a rhombus centered at the origin, with YR= 8p and PQ - 8s. What are…

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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: 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: The line segment perpendicular to the axis of symmetry, passing through the focus and with endpoints…

A: Given:The line segment perpendicular to the axis of symmetry, passing through the focus and with…

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus :…

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Q: What is the directrix, focus, and the vertex of the parabola if Vertex V (3, −2) and axis parallel…

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Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus :…

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Q: The reflector of a flashlight is in the shape of a paraboloid of revolution.Its diameter is 4 inches…

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Q: Determine the equation of the parabola using the given information. Focus (0, −3) and directix y =…

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Q: Which of the following is an endpoint of the latus rectum of the parabola with vertex (4,-2) and…

A: Topic= Parabola

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 of the parabola that satisfies the conditions. a) Focus (0, -) and directrix, y =…

A: Given  Focus (0 , -1/2)  Directrix ,y = 1/2   Equation of parabola with focus at (x0 , y0) and…

Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 1) and directrix…

A: Given that Focus of the parabola is F0, 1 and Directrix is y=-1 We have to prove that y=14x2 is the…

Q: The distance between the vertex and the focus of a parabola is called the __________ length and is…

A: First of all, consider the definition of the vertex and the focus of a parabola.The vertex of…

Q: The orthogonal trajectory of y= Ce" is a parabola of the form y = ax+b. what is the value of b so…

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Q: If the focal length of a parabola is 6 units and the vertex is (3, 2), is it possible to determine…

A: Focal length of a parabola is 6 units and the vertex is (3, 2).

Q: Why is distance between vertices for hyperbola equal to 2a?

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Q: The filament lightbulb is a thin wire that glows when electricity passes through it. The filament of…

A: Given: The given reflector is 7 inches wide and 2 inches deep i.e. (x,y)=(2,3.5)

Q: Find an equation of the parabola that satisfies the given conditions.Focus F(6, 4), directrix y = -2

A: Given: Focus F(6,4) directrix y=-2 To find: the equation

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: Find the equation of Parabola and Graph with the following information: Center at (0, 0) Vertices…

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Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus : (7,…

A: Parabola: The focus of the parabola is (7,1) Directrix of the parabola is y=-9. The equation of…

Q: The parabola has focus (0,-2) and directrix y=2.

A: equation of parabola with focus ( a , b ) and y = c  is given as below : here a = 0 b = -2  c = 2

Q: By differentiating implicitly, find the slope of the hyperboloid 22 + y? – 22 = 1 in the x-direction…

A: We have to find slope of the hyperboloid x2+y2-z2=1 in the x-direction at the points (a) 1,2,2 (b)…

Q: A sound receiving dish used at outdoor sporting events is constructed in the shape of a paraboloid,…

A: Given: A sound receiving dish used at outdoor sporting events is constructed in theshape of a…

Q: Write the equation of a parabola in standard form from the given information Focus at (-5,7)…

A: Since , focus lies on x-axis Therefore , equation is either y2=4ax or y2=-4ax Now focus has negative…

Q: which satisfies th

A: Parabola: The focus of the parabola is (-2,-5) The directrix x=6 The general form of parabola is…

Q: Find the focus diretrix, and focal diameter of the parabola: x^2=-8y

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