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

Q: Q 03: find the orthogonal trajectory of family of parabolas represented by the equation y? = 4ax…

A: Given y2 = 4ax2y dydx = 4adydx = 4a2ya = 2yy'4= yy'2y2 = 2xy dydx

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

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Q: Find the equation of the parabola with focus (5, 0) and directrixx = -5. а. b. x' = 20y c. y' = 20x…

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

Q: Find the equation for the parabola that has its vertex at the origin and has directrix at y = 7 The…

A: To find the equation of parabola that has tis vertex at the origin and has directrix at y=-17

Q: What is the standard form of the equation of the parabola with the focus (5, –1) and the directrix æ…

A: Any point at parabola is equidistant from its focus and directrix.

Q: 4. Find the focus, directrix and vertex of the parabola (x + 2)2 = 3y - 6, then sketch the curve.

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Q: - For the hyperbola - = 1, the value of a is the 4 value of b is ,and the transverse axis is the…

A: The general equation of the hyperbola is x2a2-y2b2=1.Here a is the distance from the vertex to the…

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

A: We have to find the equation of parabola where it has vertex at origin and directrix is given as:…

Q: Which of the following equations represents the parabola with vertex at (3, 2) and directrix y = 4?…

A: To find out the equation of the parabola.

Q: The focus of a parabola is (-3,5) and the directrix is y = -1. Which equation represents a parabola…

A: Given the focus of parabola is -3,5 and directrix is y=-1.

Q: For the parabola 2x-3y 0, find the co-ordinates of the focus, equation of the directrix and sketch.

A: Since you have asked multiple questions in single request. So we will answering only first question.

Q: 2. Sketch and identify the graph of the equation a + y? – 2y –- 3 = 0 in 3D.

A: x2+y2-2y-3=0x2+y2-2y+1-4=0x2+(y-1)2=4The equation represents circle in 2D,but a cylinder of radius 2…

Q: Find the equation of the parabola with vertex at the origin and focus F (0, 5)

A: General equation of parabola with vertex at origin and focus on y axis is x^2= 4ay.

Q: For the given equation of a parabola, determine the focus, vertex, and directrix. x2 – 2x – 6y + 12…

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Q: Find an equation for the indicated half of the parabola.Lower half of (y + 1)2 = x + 3

A: Given equation is y+12=x+3.

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

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Q: find the equation of the parabola with the given properties. Focus (0, 4), directrix y = −4

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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: A parabola is given by the equation y = x^2 - 4x + 6. Find k so the line of equation y = 2x - k does…

A: We have to find the value of k for which the line intersect the parabola at two distinct points. To…

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

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Q: Find the standard form of the equation of a parabola given the following conditions: a) Directrix y…

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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: Match the parabola with the following equations: x2 = 2y, x2 = -6y, y2 = 8x, y2 = -4x. Then find…

A: Given graph of parabola,

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

A: Given: The parabola has its vertex at the origin and  Directrix has y - intercept 8. We have to find…

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: Determine the equation of the parabola given the focus at (-10,23/2) and directrix at y=-11/2.

A: Given- Focus -10,232 and directrix y=-112 To Find- The equation of the parabola.

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

A: find the equation of a parabola vertex=(0,0) and directrix x=-4

Q: For the equation of the parabola (x+2) = - 16(y-4), find: a) the vertex b) the focus c) the…

A: Compare the given equation with standard equation

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 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: 1. For the parabola equation: (y-2) = -3(x+4)^2 + 7, in which direction does the parabola open? *

A: We have to find the direction in which the given parabola opens.

Q: Find an equation for the parabola shown in the figure.

A: We have given Vertex: 1, 0 Focus:6, 0   The given graph is symmetric about x-axis. Equation of the…

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

A: The formula for a parabola in vertex form is:

Q: Find the equation for the parabola that has its vertex at the origin and has directrix at x=−1/28..

A: The standard form of equation of parabola with horizontal axis is given by the formula, y2=4px…

Q: The equation of the family of parabolas with vertex and focus on the x-axis where h and k are…

A:

Q: What is the equation of the parabola shown below, given the focus at F(1, 5) and the directrix x =…

A: Here we have to find the equation of the parabola, vertex, and equation of the axis of symmetry of…

Q: 2 For the given model of the form x²=4py, (a) Determine the value of p. (b) Identify the focus of…

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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: Consider the parabola - 2.x? + 20x – 4y – 62 = 0 O What is the vertex of this parabola? (r, y) What…

A: The given parabola is:…

Q: help in 30mins pls

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

A:

Q: Find all the values of b such that the parabola y=(1)/(8)x^(2)-bx+(9)/(2) will have a directrix…

A: the given equation of the parabola is y=18x2-bx+92. we have to find all the values of b so that the…

Q: For the given equation of a parabola, determine the focus, vertex, and directrix. x2 -32y

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Q: Find an equation of the parabola with focus (15/2, 0) and directrix x= -13/2

A: The vertex will be the midpoint of (15/2, 0) and x= -13/2 So, vertex is:

Q: Find the focus and directrix of the parabola with the given equation x2 - 6y = 0. Then graph the…

A: Given parabolic equation is x2-6y=0 To find focus and directrix of the given parabola

Q: Find all values of b such that the parabola y = x² – bx + will have a directrix having an equation…

A: y=18x2-bx+92 On simplification, we get…