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

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: 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: 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 angle at which the parabola y=x2−14 intersects the positive x−axis.

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Q: Show that the center of the osculating circle for the parabola y = x2 at the point (a, a2) is…

A: We need to show that the centre of the osculating circle for the parabola y = x2 at the point (a,…

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: Find the distance between the point (p, 4p) and the parabola y? = 2px, where p is a fixed positive…

A: let the point on parabola be A= (x, y)  B = (p, 4p) Thus,  AB = x-p2+y-4p2 but parabola is y2=2px…

Q: A] Find the length of the arc of the semi-cubical parabola y2 x (1,1) and (5,5V5). 8250 between the…

A: Solution:Given        y2=x3    between the points (1,1) and (5,55)To find the Arc…

Q: Find the minimum distance from the parabola a – y? = 0 to the point (0, 3). Minimum distance =

A: Find the distance using distance formula and then differentiate to get the minimum value equate the…

Q: Find all hyperbolic lines that passes through i +1 and parallel to the y-axis.

A: Find all hyperbolic lines that passes through i+1 and parallelto the y-axis.

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: A] Find the length of the arc of the semi-cubical parabola y² = x3 (1,1) and (5,5V5). between the…

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Q: 1.) A gateway is a parabolic shape whose vertex is 20 ft. From the ground, (0,20), and the width of…

A: Given, a gateway  is a parabolic shape whose vertex  is 20 ft. From the ground, (0, 20), and the…

Q: Find b and c, given that the parabola y = x2 + bx + c passes through (0, 5) and (3, 23).

A: (0,5) means when x=0 then y=5. similarly, (3,23) means when x=3 , then y=23.

Q: Find formulas for the distances between (0, 0) and (a, a2 ), a > 0, along the line between these…

A: Derivative of a function is determined as the change of variable with respect to change in another…

Q: Find the length of the curve from the entire hypocycloid 2 2 x3 + Y³ = a³.

A: Explained below

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 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: Find the length of the arc of the semicubical parabola x  sq = ycu . betweenthe points (2,2 )  ; (4,…

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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: At what point does the normal to y = 3x – (5 + 4x) at (1, –6) intersect the parabola a second time?…

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Q: 4 SKetch the parabola and label the foces , ventees and dineder 2. 4 -6y -2utl=0

A: To find- Vertex, focus and directrix of a given parabola.

Q: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

A: Consider the given parabola y2=4ax Suppose Ax1 , y1  and  Bx2 , y2 be the ends of the focal chord of…

Q: Find the area of the segment cut off from the parabola x2 = 8y by the line x- 2y + 8 = U. %3D

A: Introduction ::

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

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Q: a. Find the length of the arc of the semicubical parabola ay=x' , from x= to x= 5a.

A: Arc length of the curve

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: 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: 1. Let P(r1, y1) be a point on the parabola r? be the angle between the parabola and the line…

A: angle with a curve at a point means angle with tangent line at that point of curve .

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: 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: x ds, where C is the portion of the parabola from (0,0) to (1, 1), followed by the line segment from…

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Q: Find the directrix for the parabola. y = 20 (x+ 2)² - 3 1- x= -1 O y = -1 O y = -8 y 3= O x = -8

A: We will find out the required equation of directrix.

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: If a parabola defined by f(x)=2−x2 is inscribed under equilateral triangle ABC, so that the parabola…

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Q: =r such that the point (2, 1) is on the segment AB and the midpoint of Determine the coordinates of…

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

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Q: b. the length of the tangents from the point (2, 5) to the circle x +y² -14x-2y+34= 0

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Q: Find an equation for the set of points equidistant from the y-axis and the plane z = 6.

A: we  have to find an  equation for the set of points equidistant from the y-axis and the plane z =…

Q: A spotlight is made by placing a strong light bulb inside a reflective paraboloid formed by rotating…

A: Let's find how far from the vertex should the bulb be placed.

Q: Find the x intercept(s) and the coordinates of the vertex for the parabola y = x^2 – 2x + 1. If…

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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…

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Q: Find the shortest distance of the point (10,4) to the parabola y=x2

A: Consider a  point on parabola  y=x2. Distance of this point with (10,4) s2=(x-10)2+(y-4)2…

Q: 6. Show that if m is any real number, then there are exactly two lines of slope m that are tangent…

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

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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: If P(a, a²) is any point on the parabola y = x², except for the origin, let Q be the point where the…

A: To Determine: If P(a,a2)is any point on the parabola y=x2,except for the origin,let Q be the point…