The line x=C where C70 intersects the cubic y= 2x3 + 3x²-9 a七 the point P and parabola y = 4x+ 4x +5 2. at %3D point Q.

Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope −12 at x = −1, and…

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Q: Determine the general equation of a parabola opening downwards whose vertex is at (3,-4) with a…

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Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle ² +y² = 13.

A: We use formula of Lagrange's multiple Del(f(x)) = lamda * del(g(x))

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: Find a parabola with equation  y = ax2 + bx + c  that has slope  13  at x = 1, slope  −19  at x =…

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Q: Find the largest rectangle (that is, the rectangle with largest area)that fits inside the graph of…

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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: In the xy-plane, a line that has the equation y = c for some constant c intersects a parabola at…

A: in the xy-plane a line that has the equation y=c for some constant c intersects a parabola at…

Q: 4. Determine the slope of the common tangent to the parabolas y=x² +1 and y=-x² - 1. y=x*2+1 (a, b)…

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Q: Find the asymptotes of the cissoid of Diocles defined by the equationy2(2a−x)=x3,a&gt;0.

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Q: 13. The parabola y = x2 + x + 1 opens: A. To the right %3D B. To the left C. Upward D. Downwarč

A: y=x2+x+1 here parabola is in the form of y=ax2+bx+c which means it can be open up or down…

Q: What can you say about the inflection points of a cubic curve y = ax3 + bx2 + cx + d, a ≠ 0? Give…

A: To find the point of inflection, we find the values of x for which the second derivative of 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: The area bounded by the parabolas (x − 2)^2 − 9py=0 and y^2=9p(x−2) is to be revolved around x = 2.…

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Q: Show that the number 4p is the width of the parabola x2 = 4py (p&gt;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: 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 points on the parabola y=x^2 closest to the point (0,1)

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Q: Find a parabola with equation y= ax2 + bx +c that hasslope 4 at x=1  , slope -8 at x= -1 , and…

A: The parabola is y=ax2+bx+c. It has a slope of 4 at x=1 and slope of -8 at x=-1 and passes through…

Q: Find the point on the parabola y = (x – 3)² – 5 that is closest to the point (0,0). |

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Q: Sketch the graph of the cylinder given by 4x2 + 9y2 = 36. show solution

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Q: Find the tangent line to the parabola x2-6y=10 through (3,5) (ILLUSTRATE SOLUTION)

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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 point on the parabola y = x³ that is closest to the point (1, 2) with two digits accuracy…

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Q: The region in the first quadrant bounded above by the parabola y = x², below by the x-axis and the…

A: Aa per our guideline we are allowed to do 1 question or 3 subparts at a time. Please post other…

Q: The shortest distance between the parabolas y² = x – 1 and x' = y-l is V2, then the value of…

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Q: Find the point(s) on the parabola x =y closest to the point (0,3)

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Q: (3) Find the coordinates of the points of intersection of the parabola y = x2 - ax and the line y =…

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Q: Q,9. What point on the parabola y = v2x + 5 comes closest to the ori

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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 point on the parabola x = t, y = t2, -∞ &lt; t &lt; ∞ closest to the point (2, 1/2).

A: Given Data The first equation is x=t. The second equation is y=t². The point is (2,1/2).…

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: Find the point on the parabola y=x2 closest to (6,3

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Q: Evaluate x° ds where C is the part of the parabola y = x² from (0,0) to (2, 4).

A: Form the double integral and set the limits than integrate with respect to y and x.

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 c > 0 such that the area of the region enclosed by the parabolas y = x^2 - c^2 and y = c^2 -x^2…

A: Given parabolas, y=x2-c2y=c2-x2

Q: The region in the first quadrant bounded above by the parabola y = x ^ 2 below by the x -axis, and…

A: Follow the steps.

Q: Evaluate (x - iy) dz along (a) the parabola y = 2r? from (1, 2) to (2, 8),

A: In the given problem we have to evaluate  ∫C(x2-iy2)dz  along the parabola  y=2x2 from (1,2) to (2,…

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: Consider the parabola f (x) = x² – 4x and the line g(x) = –2x – 1. Determine the %3D point(s) of…

A: Given parabola,y=x2-4x                     (1)Given line y=-2x-1                     (2)Put value of…

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: 1. Find the point on the parabola y = 3 – x² that is closest to the point (6, 0).

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Q: Find the point P on the parabola y = x2 closest to the point (57, 0). (х, у) %3D ]-«

A: Given the equation of parabolay=x2         ........(1)

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: I For the parabola -2x = 16y + 4y² + 13, for what value of y does x have a minimum? 3. If the

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Q: The maximum vertical distance between the parabola y = 3-z and the line y = 3x+2 on the interval…

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Q: Find the parabola with equation y = ax? + bx whose tangent line at (2, 8), is y = -2x + 12.

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Q: 33) Find the points of intersection between the line x - y - 2 = 0 and the parabola y = 4 - x 2.

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Q: Find the points on the curve x2y = 2 nearest the origin.

A: The curve is x2y=2 Let x1,y1 and x2,y2 be two points, distance betwwen these points is x2-x12+y2-y12

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.