1. Find the value of k such that the perpendicular distance of the point (2,k) from the line x - 2y = -3 is square root of 5.  A.10 B. -10 C. -5 D. 5

Q: What is the equation of a parabola with vertex at (0,0), opens to the left and the length of latus…

A: Explanation: Given that,  Vertex of the parabola is (0,0) and the length of the Latus Rectum is 6…

Q: What is the length of the latus rectum (LR) of the parabola y = -÷(x – 2)“ + 5?

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Q: What is the nearest distance from the point P(6,0) to the parabola? y^2=8x

A: GivenP(6.0)y2=8x To find nearest distance

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: As xx, f(x) →∞, and as x →∞, f(x) →→∞

A: Given the equation is f(x) = -3x2-4x+7

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

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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 equation of the directrix of the parabola having a vertex at (6,0), passing through…

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Q: For Exercises 13–14, the graph of a parabola is given. a. Determine the distances di, d2, d3, and…

A: The graph of parabola is given below. Determining the distance d1,d2,d3and d4.  d1 is the distance…

Q: Find the point on the parabola y* = 2x that is nearest the point (1, 4).

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

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Q: Suppose you are given the x-coordinate of a point on a parabola. How can you find the matching…

A: According to Bartleby guidelines, only one question can be solved at a time. Kindly post other…

Q: Find the vertex of the given parabola. Give all values correct to 3 decimal places. y = 7x2 - 8x +…

A: A detailed solution is given below

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

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Q: What is the equation of the parabola that opens to the right and with vertex at (4,-2) and a latus…

A: Prabola

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: "X" raised to two equal to sixteen times "y" is an upward parabola with vertex at the origin. (A)…

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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 a point on the parabola y - x* + 9 which is closest to the origin.

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Q: Find the coordinates of the point on the parabola y = x² which is closest to the point (3, 0).

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Q: Find the area of the largest rectangle with the lower base on the X-axis and the upper vertices on…

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Q: Suppose that point A(-4,0) lies on a parabola whose focus is at (5,3). What is the length of the…

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Q: The equation of the parabola that has a vertical axis of symmetry, touches the line y= 6 and has its…

A: Your 3rd option is your correct option...detailed solution I have done step by step in…

Q: The parabola y = x² is shifted up by 7 units and to the left by 1 unit. What is the equation of the…

A: Equation of parabola is given as y=x2. If the parabola is shifted by a units and to the left by b…

Q: What is the equation of the parabola in general form given its vertex at (-1,-5) and focus at…

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Q: Find the shorted distance from the point A(2, to a point on the parabola y = x². And find the point…

A: Let (x,y) = (x,x2) point on the parabola is closest to A Distance between (2 , 1/2) and (x,x2) is:…

Q: A parabola with a negative latus rectum has endpoints at (5, 1) and (5, -11) Where is the vertex? *

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Q: Graph the parabola and the tangent line. As a check on your work, zoom in toward the point (-3, -12)…

A: Given-  To graph- The parabola and tangent line which is passing through -3,-12.

Q: if the point (a, b) is on the parabola y=6x^2-(5785/12) that is closest to the point (0,4) than a ?

A: Given, y=6x2-578512 suppose x,y any point closest to 0,4  D=x-02+y-42 put y in equation,…

Q: What are the coordinates of the end points of the latus rectum of the parabola with equation a - 2z…

A: What are the coordinates of the end points of the latus rectum of the parabola with equation…

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

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Q: Find the standard equation of a parabola if its latus rectum measures 9 units, axis at y = 3, p is…

A: Let's find standard equation of a parabola.

Q: Find the point on the parabola y 2 =2x that is closest to the  point ( 1, 4)

A: Given: y2=2x let's point on parabola is t22,t now, if point1,4 is closest to t22,t2 then product of…

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

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Q: What is the standard form of the equation of the parabola with the focus (-3, 6) and the directrix y…

A: GIVEN: focus (-3, 6) Directrix y = -2

Q: If the parabola whose equation is x = ay2 + by + c has its vertex at (3,2) and a> 0, then it has…

A: The given statement is that" if a parabola whose equation is x=ay2+by+c has its vertex at 3,2 then…

Q: The parabola y=x^2y=x2y, equals, x, squared is shifted up by 777 units and to the left by 111 unit.…

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Q: 9.  Find the shorted distance from point A(2, 1/2) to a point on the parabola y = x2. And find the…

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Q: Find the minimum distance from the point (4, 2) to the parabola y2 = 8x. A 4/3 B) 2/7 © V3 D 2/3

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

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

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Q: Find the equation of the parabola that is symmetric about y axis with vertex at the origin and…

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Q: Express your final answer in Mdx + Ndy = 0 1. Parabola whose vertex is at point P(13, 60).

A: The given data is: 1. Parabola whose vertex is at point P (13,60), Express your final answer in…

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

A: At the points of x-intercepts, y coordinates are 0, as along x-axis y=0.

Q: What is the length of the latus rectum of the parabola: y2 – 4y – 8x – 28 = 0?

A: Given, y2 – 4y – 8x – 28 = 0 General equation of parabola with center (h,k) (y-k)2=4a(x-h)    ---(i)

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: 6. After a reflection in the x-axis, the parabola y =x -4 would have the equation (1) y=x²+4 (3)…

A: Reflection in x axis

Q: 4. What is the focus of the parabola whose equation is -(y- 3)2 = (x – 2)? O A. (2, 1) OB. (0, 3)…

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