A parabola is opening downward, always having a length of latus rectum equal to 4. The vertex of this parabola always exists at the line x = 2. An orthogonal trajectory intersects this parabola at the y - intercept of 1. The vertical asymptote of this orthogonal trajectory to the parabola is located at x = _______. If decimals, use 8 decimal places.   Pls. write the solution neatly

Q: Find the following points of intersection. The point(s) of intersection of the parabolas y = x2 and…

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Q: (a) Suppose that a > and that the parabola with equation y = ax? +2 has vertex V. The parabola…

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Q: 2. Circle the parabolas that are stretches of the graph y = x². а) у3 1.25х? c) y = – x? b) y = 0.25…

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Q: P(0, -1) from the point (x) = x² + 2x Apses of the points where the tangents drawn on the parabola…

A: The given equation of the parabola is, fx=x2+2x Apses of the points means that two lines meet at…

Q: 2=2X Find the point that is close' to the pont'(,4) on the parabola y

A: Explained below

Q: Find a parabola with equation y = ax + bx +c that has slope 7 at x = 1, slope -25 at x = -1, and…

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Q: A parabola has an equation of y² = 8x. Find the equation of the tangent to the parabola having a…

A: Use equation of tangent line of parabola and put value

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: Given that the vertex of a parabola is (-3,3) and a =4. Find the vertex form of the parabola. f (x)…

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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 a parabola with equation y = ax? + bx + cthat has slope 4 at x-1, slope -8 at x=-1, and passes…

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

A: Here we have to find the equation of the parabola that has its vertex at the origin  and Directrix:…

Q: Q13:- Given a parabola y? P1 tangent to the parabola. Find the area of the triangle A0AB = 4px, and…

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Q: A parabola has an equation of x2 = 6y + 10. Determine the equation of a diameter of the parabola…

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

Q: Find the y-intercept of the tangent to the ellipse x + 3y = 1 at the point %3D 1/2

A: We differentiate both sides with respect to x and then solve for dy/dx

Q: Find the equation of the osculating circle of the parabola y= 1 x' at the point where x = 1. Then 4.…

A: The given data is: The equation of a parabola is: y=12x2 To find the equation of the osculating…

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: The line y = 8.5x+5 intersects the parabola (y-4) = (x-6)2 at points A and B. Point C is on the…

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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: Find the shortest distance from the point (1,4) to a point on the parabola y =2 x (a) /2 (b) 1 (c) 2…

A: To determine the shortest distance between point and the parabola,

Q: How many derivations are required to find the DE for parabolas with axis parallel to the x-axis and…

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Q: Let F(r, y) = (x + 1)7, and let C be the portion of the parabola y = x² that starts at (0,0) and…

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Q: . Find the point on the parabola y = x² closest to (6,3). newor: The noint is (24)

A: Given curve is y=x2

Q: Find the shortest distance +rom the point (0,5)to the ellipse 3 y? = x'

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Q: Given the parabola x^2=4y, a line passes through point A (4,4) and the focus of the parabola. Find…

A: Topic:- Parabola

Q: (x, y)  =           x-intercept (x, y)  =             (smaller x-value) x-intercept   (x, y)  =…

A: We Can make it easier for you.

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: A parabola has a focus of (4, −5) and the directrix is ? = 8. Which of the following functions model…

A: Explanation of the answer is as follows

Q: 5.Find the point on the parabola x? = 4y nearest to (0,4).

A: Given:      x2 = 4y    Point : ( 0 , 4 )

Q: With reference to the parabola y?-2x+6y+ 9 = 0, find the values of k for which the lines of the…

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Q: Find the following points of intersection. The point(s) of intersection of the parabola y = x2 + 2…

A: Given equation of parabola is y=x2+2 and equation of line is y=x+4. We have to find point of…

Q: Use the graph of the parabola to fill in the table. (a) Does the parabola open upward or downwa O…

A: a.   Parabola opens downward   b. Coordinate of vertax. Is (-2,-3)

Q: The distance between the towers of the main span of the Golden Gate Bridge is about 1280m; the sag…

A: We have,  y=143m,   x=12802

Q: shortest distance from the point (0,6) to the parabola x² – 4y = 0.

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Q: Find ? for which the line tangent to the parabola ? = 4? − ?^2 is horizontal

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Q: The normal to the parabola y2= 4ax at the point P(at2 , 2at) meets the x-axis at A. Find the…

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

A: Please refer the attached image for complete solution.

Q: ind the vertex and the x-intercepts (if any) of the parabola. (If an answer does not exist, enter…

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Q: To y=x²-12x + 20 Parabola Wite the intersection point of the tanpent lines drawn from (2,0) and…

A: Consider the given parabola and find the derivative of the parabola.…

Q: Not so long ago, you learned in this course that the vertex of the parabola y = ax? + b bx + c…

A: iven equation of parabola, Y= ax2 + bx +c

Q: A parabola has a vèrtex at the origin and a focus of (0, 3/2). What is the equation of the parabola.

A: The general equation of a parabola with vertex at origin is given by y2=4ax. The distance between…

Q: A parabola having its x axis parallel to the y-axis has its focus at (5,6) and vertex at (5,4).…

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Q: Use the 1 of the parabola to fill in the table. 10- (a) Does the parabola open upward or downward?…

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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: ind the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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

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Q: 1) Find the intercept(s) and vert ex of the parabola. y=x^2-1

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Q: Determine the following details about the parabola associated with the equation y = (x + 2) – 16.…

A: Solution: The objective is to find the vertex of the given parabola

Q: 3) Assume that the parabola y=x is translated so that its vertex is (5,-4). I If the parabola is…

A: Let's see a concept of stretch of function y=f(x). Say y = f(x) is parent function.