Find the equation of the parabola and the length of the latus rectum with directrix y = -2 and focus at (0,2). Sketch graph.

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: Find the equation of the parabola with a focus at (1, -8) and a vertex at (1, - 2). Let a represent…

A: Since the x-coordinates of the vertex and focus are the same, they are one of top of the other. So,…

Q: at

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

Q: Graph the given parabola and find its focus: Y=X squared

A: The given equation of parabola is: y=xory2=x  where x > 0

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

A: First we have to calculate distance from directix to vertex. I.e P Then insert values of center and…

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus: (0,…

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

A: Given: Opens downward with focus 10 units away from the vertex.

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

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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: Find an equation for the parabola with focus (0, -4) and directrix y =

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Q: The parabola y=x^2+13 has it's focus at the point (b,c) where  b= c=

A: The given equation of the parabola is, y = x2+13. Also the parabola has its focus at (b, c).Consider…

Q: State the equation of the parabola which has a focus of (9, 3) and a directrix of y = -3. (Let a be…

A: To find the equation of the parabola having focus and a directrix, let we choose (x, y) be any point…

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: Find the equation of parabola with rertex at (0,0 and focus at (3

A: Given the vertex is at(0,0) and focus (3, 0)

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

A: Given: Focus on the negative y-axis, 6 units away from the directrix

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

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Q: Find the focal diameter of this equation:   y^2=32x   also sketch a graph of the parabola and…

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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: Use the Distance Formula to write an equation of the parabola with focus F(0. 9) an y%3D

A: Topic- equation of parabola

Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus : (0,…

A: given, focus (0,15) directrix y=-15

Q: 2. Find the equation of the parabola described. a. Vertex at (4, –2); focus at (6,–2) b. Focus at…

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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: find the equation of the parabola with the given  Focus (2, 0), directrix x = −2

A: Our Aim is to find the equation of the parabola with the given Focus (2,0) and directrix x=-2.

Q: Find the equations of the osculating circles of the parabola y = 3(x – 2)2 at the points (2,0)

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

A: Given- The parabola that has its vertex at the origin and satisfies the given condition(s).…

Q: Find an equation of the hyperbola that has foci at (0, -10) and (0, 10), and asymptotes y = 1 x and…

A: To find the equation of hyperbola

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

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Q: Find the general form and graph of the focal width of a parabola is 14 units and its vertex can be…

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Q: Find the point(s) on the parabola x =y closest to the point (0,3)

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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: 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: Find an equation of the parabola deseribed. Focus at (5, 0); vertex at (0, 0) O y = 20x2 O x = 20y O…

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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: Find the standard form of the equation of the parabola satisfying the given conditions: Focus : (0,…

A: Given:Focus0,20Directix y=-20Parabola:x-h2=4p y-k

Q: Find an equation of the parabola with focus (4, 4) and directrix x=0.

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

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Q: given the directrix of y = 6 and focus of (0,40, which is the equation of the parabola?

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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: Find an equation of the parabola that satisfies the given conditions.Focus F(-3, -2), directrix y =…

A: We have given the equation of directrix is y=1 which parallel to the x-axis. The standard equation…

Q: Find the focus, directrix, and focal diameter of the parabola y = x², and sketch its graph.

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Q: Find the equation for the parabola that has its vertex at the origin and has directrix atI = 27…

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Q: Find the standard form of the equation of the parabola satisfying the given conditions: Focus : (2,…

A: Consider trhe focus of the parabola is 2,4 and the directrix is x=-4. Let x,y be any point on the…

Q: Find the equation of the parabola with a focus at (0, 5) and a vertex at the origin. Let a represent…

A: The solution is :

Q: Determine the equation and sketch the graph the parabola given focus at (12, 3) and directrix at x =…

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Q: Which is the equation of a parabola with a directrix at y = 2 and a focus at (5, 0).

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