(0, b) Figure for 1(b) 2.

Q: Find the family of curve that intersects the family of hyperbolas y² = 2x² +b at an angle arctan(1).

A: To find the family of the curve that intersects the family of hyperbolas y2=2x2+b at an angle…

Q: Find the equation of the parabola and the length of the latus rectum with directrix y = -2 and focus…

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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: b) Consider now the portion of the parabola which is below the line y = 2. Which points have the…

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Q: 5. The equation of a family of parabolas with axis paralel to the y-axis is 6. The equation of the…

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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 equation of the parabola with vertex at (0, 0) and directrix y = -8 in standard form?…

A: Given that, vertex of parabola is (h, k) = (0, 0) diretrix of parabola is, y = -8 We have to find…

Q: Do I have to use the equations for the asymptotes of a hyperbola centered at the origin, y = tr or y…

A: The equations for the asymptotes of a hyperbola centered at the origin is y = ±bax or y = ± abx.…

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

A: equation of parabola:-

Q: Find an equation for the curve traced by the point P(x, y) if the distance from P to the vertex of…

A: First find the vertex and focus of x^2=4y

Q: The area of the triangle formed by the tangent and the normal to the parabola y = 4ax both drawn at…

A: Given  the parabola y² = 4ax both drawn at the same end of the latus rectum and the axis of the…

Q: What is the measure of the focal width of the parabola y+2y+4x-3=0 ?

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Q: What is the family of curves for all parabolas with axes parallel to the y-axis.

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Q: Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8. 1 O f(x) -(x –…

A: Given query is to find the equation of parabola.

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

A: Given vertex is (0 , 0) and focus on negative y axis focal diameter is 2

Q: 2. Parabola with x+1= 0 as the directrix, y = 1 as the axis, and the length of the latus rectum is…

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

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

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Q: b) Sketch the parabola with the graph cuts the x-axis at (5,0) and (-5,0), the directrix line y = 4…

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Q: Find an equation for the parabola with vertex V(0, 0) and Focus F(0, 2), and sketch its graph.

A: We have given vertex V0,0 and focus F0,2. Given the vertex of the parabola is V0,0 and focus is at…

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

A: It is given that the Vertex is V(0, 0) The focus is on the positive x axis, 2 units away from the…

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: Determine the area of the largest circle that can be enclosed by the two hyperbolae, xy= 1 and xy =…

A: Solution is here

Q: On a separate piece of paper, sketch the graph of the parabola y = x + 3. On the same graph, plot…

A: Given: Equation of parabola, y=x2+3

Q: Sketch the parabola y = x² + 2x +1. Use arrows to indicate the maximum and minimum values of y over…

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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: The centre of a circle C lies at the focus S of a parabola y2 = 4x and the radius of C is equal in…

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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: Sketch parabola y = x2 – 10x + 16 by plotting a few points to left and right of the vertex. (Find…

A: Given parabola y=x2-10x+16                  ....(1)

Q: Find the standard equation of the hyperbola with the stated conditions. Vertices at (2,-5) and…

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Q: Find an equation of the hyperbola that has fodi at (-15,0) and (15, 0), and asymptotes y=x and y =

A: here we have to find the equation of hyperbola that has foci  at (-15,0) and (15,0) asymptotes…

Q: Find the y-intercept and any x-intercept(s) of the parabola with equation y = -(x + 7) + 16. If the…

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Q: 24. Construct the equation of a parabola with focus at (-1,2) and a directrix x = -7.

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Q: Find the minimum distance between the point (5,1) and the parabola y=-x2 ?.

A: Find the minimum distance between the point (5, 1) and the parabola y = -x2?

Q: 1. Consider the parabola whose directrix is at x = -7 and whose focus is at (-1, 1). What is the…

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Q: [1] What is the c value of a parabola with a Vertex of (4,2) and a Focus of (4,4)?

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

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: 21 Find the equation for the parabola that has its focus at the 2 and has 4 11 directrix at æ = 4…

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Q: 28. Find the directrix for the parabola. (y+ 3)2 + 8 2x x = 4 y = } 7/2

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Q: 1. Which of the following best describes the graph of y = x? – 4x + 2? a parabola with a vertex at…

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Q: Two parabolas are given: - C₁ is the curve of intersection between y = 1-2² and 2 = - C₂ is the…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: What is the equation of the parabola with vertex at (0, 0) and directrix y = 3 in standard form.…

A: Given vertex 0,0 and directrix y=3. We have to find equation of parabola.

Q: Plot both the following curves on the same set of axes. r = 5 − 4cos(θ), and the parabola y = x².

A: We have to Plot both curves on the same set of axes. r = 5 − 4cos(θ), and the parabola y = x².

Q: 20. Parabolas with vertex and focus on the x-axis. llel to the y.

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Q: Find the general form and graph of the vertex of a parabola is at (-2, 0 with a latus rectum, that…

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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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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.