In Exercises 5–-16, determine the coordinates of the focus and the equation of the directrir of the given parabolas, Sketch each curve.

Q: Which is the equation of a parabola with focus (0, 5) and directrix y= -5?

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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: 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: In Exercises 1-18, graph each ellipse and locate the foci. = 1 4 2. 1. 16 + 25 16 3. 9 36 4. 49 5.…

A: To graph the ellipse and locate the foci. 1) x216+y24=1 Major axis is x-axis and the minor axis is…

Q: Find the standard form of the equation of th parabola with: and Focus (-2, 6) Directrix X = 8

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Q: What is a parabola? What are the Cartesian equations for parabolas whose vertices lie at the origin…

A: What is a parabola? What are the Cartesian equations for parabolas whose vertices lie at the origin…

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: In Exercises 19-24, find the standard form of the equation of each ellipse and give the location of…

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Q: in exercises 37-50, find the vertex, focus, and directrix, of the parabola. then sketch the…

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Q: In Exercises 17-30, find the standard form of the equation of each parabola satisfying the given…

A: The standard form of the parabola is (x-h)2=4p(y-k) this equation is open upward or downward its…

Q: Which is the standard equation of the hyperbola centered at the origin, with a vertical transverse…

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Q: Consider the parabola whose vertex us at (2,-1) amd focus at (0,-1). What is the general form of the…

A: Given, The vertex of the parabola = 2, -1  Focus of the parabola = 0,-1 We have to write the general…

Q: the chord joining points the A(x) and B(B) on the hyperbola -= 1 is a focal chord, then prove at…

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

A: Consider the following values: Focus=9,0Diretrix⇒x+9=0 Standard form of the equation of the…

Q: Determine the focal distance of a hyperbola if the length of the transverse and conjugate axes are…

A: The focal distance of a hyperbola is 17units.

Q: In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation.…

A: Since you have posted multiple question , we will solve the first question for you . If you want any…

Q: 16. х2 — 2х — 4у — 7 %3D 0

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Q: What is the standard form of the equation of the parabola with the focus (6, –1) and the directrix x…

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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: For Exercise, determine the standard form of an equation of the parabola subject to the given…

A: Given directrix: x=0 and focus (-4,5)The vertex will be the mid point of them Mid point of x=0 and…

Q: In Exercises 17–30, find the equations of the parabolas satisfying the given conditions. The vertex…

A: Given vertex (0,0) and directrix y=-0.16 We know the standard form of parabola with vertex at origin…

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: In Exercises 5-16, determine the coordinates of the focus and the equation of the directrix of the…

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Q: In Exercises 11-18, find the standard form of the equation of the ellipse with the given…

A: Since you are asking multiple questions. As per our guidelines, we are supposed to answer only one…

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

A: To find the equation of the standard form of parabola Focus -10,0 Directrix x=10

Q: A parabola has an equation of y² = 4x. Find the nearest distance from the point (-3, 6) to the %3D…

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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: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

A: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

Q: What is the equation of the standard hyperbola with vertices at(0, ±a) and foci at (0, ±c)?

A: Given-  Hyperbola with vertices at (0, ±a) and foci at (0, ±c). To find- The standard equation of…

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: Match the parabolas in Exercises 1-4 with the following equations: x? = 2y, x2 = -6y, y? = 8x, y? =…

A: To match the following equations, with the graphs of parabolas and find its focus and directrix,

Q: What is the equation of the parabola with vertex at (0,0) and focus (0, –4) in standard form?…

A: see below the calculation

Q: For Exercise, an equation of a hyperbola is given. Determine whether the transverse axis is…

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Q: Define the term parabola?

A: Given: The term parabola.

Q: Find the standard form of the equation of the parabola. Focus at (0, 4), directrix y = -4

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Q: Determine the standard equation of the ellipse that satisfies the given properties: center at the…

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Q: Explain why the dots in Figure 23 lie on a parabola. Where are the focus and directrix located? y=…

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Q: Determine the coordinates of points A and B on a parabola y midpoint of AB is as close as possible…

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Q: Which is the corresponding equation of the hyperbola with foci located at (-8, 0) and (8, 0) and a…

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Q: Hyperbola: x = h + a sec 0, y = k + b tan 0

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Q: For Exercise, determine the standard form of an equation of the parabola subject to the given…

A: Plot the given points line joining focus and vertex is parallel to y axis. That means axis is…

Q: Find a Cartesian equation for the hyperbola centered at the origin that has a focus at (3, 0) and…

A: The focus is 3,0 c,0=3,0∴c=3 Also the directrix x=ae=1                           ∴a=e Now…

Q: Determine the standard equation of the ellipse that satisfies the given properties: 16 3, horizontal…

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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 a Parabola with directrix x = 3/2 and focus (5/2 , 4)

A: The given problen is solved below in detail.

Q: Derive an equation for the parabola with focus (a , b) and directrix x = c

A: Given focus f =(a,b) and directrix x=c Let A(x1,y1) be any point so that  |Af|= |AD| Where Af=…

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: 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: 40. y² – 16x² + 64x 208 = 0

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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: Find the standard form of the equation of the parabola with the given characteristics. Focus: (1,…

A: Given: A rough sketch of the parabola shall be as follows:

Q: Which is the corresponding equation of the hyperbola with foci located at (−8, 0) and (8, 0) and a…

A: Given data is : Foci are -8,0 and 8,0 The transverse axis is 14 unit

Q: What is the geometric interpretation of b/a in the equation of a hyperbola in standard position?

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Q: Given an ellipse x2/a2 +y2/b2= 1, a  b, find the  equation of the set of all points from which there…

A: (Note: We are entitled to solve only one question at a time) Given: x2a2+y2b2=1, where a≠b. To Find:…

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.