=r such that the point (2, 1) is on the segment AB and the midpoint of Determine the coordinates of points A and B on a parabola y AB is as close as possible to the ordinate axis.

Q: Determine the value of p (where Ip| corresponds to the distance from the vertex to the focus) of the…

A: Given: Vertex of parabola is 3, -6and y-intercepts are 0, -10 and 0, -2. To determine: Value of p.

Q: For Exercise, find an equation of the form  y = ax2 + bx + c that defines the parabola through the…

A: Consider the given equation of parabola:

Q: dr if F= and C is a piece of the parabola y=4-x² from the point (–1,3) to the point (2,0).

A:

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

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Q: Let P and Q be distinct points on the parabola y = 2r such that a circle with PQ as diameter passes…

A: The given equation of parabola y2=2x Let P and Q be points on the parabola  Parametric coordinates…

Q: Find the point on the parabola x= - 2t, y = - 2t, - o <t< oo, closest to the point (- 32, – 1).

A: Let the point (x, y)=(-2t, -2t2) on the parabola be the closest point to (-32, -1) So distance…

Q: Compute the length of the latus rectum of the parabola y2 + 8x – 6y + 25 = 0.

A:

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: Please

A: Now differentiate it with respect to y and equate it to 0.

Q: Find the equation of the directrix and the length of the latus rectum of the given parabola.…

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

A:

Q: In the xy-plane, if the parabola with equation y = ax² + bx + c, where a, b, and c are constants,…

A:

Q: Determine the value of p (where |p| corresponds to the distance from the vertex to the focus) of the…

A: Given: Parabola whose vertex is 6, 7 and the x-intercepts are 3, 0 and 9, 0. To determine: Value of…

Q: Where does the line x = 1 + 3t, y = 2−t intersect (a) the x-axis (b) the y-axis (c) the parabola y =…

A: Parametric equations are a set of equations where 2 or more variables are dependent on one single…

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

A: Explained below

Q: a. If a chord of the parabola y² = 4ax a normal at one of its ends, show that its mid- %3D y?, 8a3…

A:

Q: Find the standard form of the equation of the parabola with the given characteristic and vertex at…

A:

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

A:

Q: Which of the following equations of parabolas has its vertex at (1, 2)? O y= 12 + 2x + 3 O y= r² +…

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Q: Find the endpoints of the latus rectum of the parabola below. 1 (v – 1)? 20 (x + 2) : Enter the…

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

A: Given thatthe vertex of the parabola at the origin and focus is(0, -1/2)

Q: Find the x-intercept(s) and the coordinates of the vertex for the parabola y=x²-8x+7. If there is…

A: The given equation is;  y=x2-8x+7.

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: Arrange the parabolas represented by the equations according to the positions of their foci on the…

A: The standard form of a parabola is  (x – h)2 = a(y – k) where (h, k) is the vertex.

Q: Find constants a and b so that the minimum for the parabola f(x) = x + ax + boccurs at the point…

A:

Q: Find the point on the parabola (y = x2/2) that is closest to the point (-4,1)

A: Use distance formula to evaluate

Q: - Find a parabola with equation y = ax? + bx +c that has slope 4 at x = 1, slope –8 at x = -1, and…

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Q: Find the vertex, focus and endpoints of the latus rectum of the parabola  4y^2 - x + 2 y = 0

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Q: Find the point(s) of intersection of the parabolas y =x2 andy = -x2+ 8x.

A: Definition used-      Point of intersection-           For finding the point of intersection of…

Q: Find the x-intercept(s) and the coordinates of the vertex for the parabola y=x+4x-5. If there is…

A: The given parabola is: y=x2+4x-5...(1)

Q: The value of y dæ – x dy where C is the portion of the parabola y = x² – 1 from (0, –1) to (-2, 3)…

A:

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: The points P(ap2 , 2ap) and Q(aq2 , 2aq) lie on the parabola y2= 4ax. Prove that if PQ is a focal…

A:

Q: A parabola is defined as being the locus of points P(x, y) that satisfy FP= MP, given coordinates…

A: Formula of the distance of two points x1,y1 and x2,y2 is: d=x1-x22+y1-y22 Here, FP is the distance…

Q: Find the length of the parabola given by c(t) = (t, t2) for 0 ≤ t ≤ 1.

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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: For hyperbola represented by 16x? – 3y?- 32x + 12y- 44 0, which | of the following is false. O…

A: For the solution follow the next step.

Q: For the three points ( 1,5), (2,9) and (-1, 7), find a quadratic model y = ax + bx + c through the…

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Q: The parabola y = Px² + Qx + R_passes through the coordinate (1,1) and has b. Determine the values of…

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Q: Find a or k so that the points (-5,-8) and (1,-25) lie on the parabola y=a(x+3)²+k

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Q: The area of the region to the left of the parabola x=2y^2, to the right of the y-axis, and between…

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Q: Evaluate a ds, where C is the parabola i = (3t, 3t2), for – 1 <t < 1. Answer exactly or round to 2…

A:

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…

Q: 2. Find the point on the parabola x+y? 0 that is the closest to the point (0, -3).

A:

Q: Find the x-intercept(s) and the coordinates of the yertex for the parabola y =x´ +4x+4. If there is…

A: The given parabola is: y=x2+4x+4 To find the x-intercept and the coordinate of the vertex for the…

Q: For Exercise, determine the standard form of the parabola subject to the given conditions. Vertex:…

A: To determine the standard form of the parabola.

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

A:

Q: Determine the coefficients a, b, and c of the parabola y = ax² + bx +c that passes through the point…

A: Solution is here

Q: Find the vertex Focus and divertrix to given the parabola x2 +6x+8y+25-0

A: The given equation is: x2+6x+8y+25=0 That can be written as…