The maximum vertical distance between the parabola y = 3-z and the line y = 3x+2 on the interval where the parabola is above %3D the line is units.

Q: Find the coordinates of the vertex of the parabola y = x^2 - 4x + 1 using derivatives O (2, -3) O…

A: To find the vertex of the parabola by using derivatives

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: 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: Find a parabola with equation y = ax2 + bx + c that has slope 11 at x = 1, slope -25 at x = -1, and…

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Q: Find the standard equation of the parabola with x intercepts at x = 2 and x -3, and a y-intercept at…

A: Solution is given below

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: Find an equation for the curve traced by the point P(x, y) if the distance from P to the vertex of…

A: First find the vertex and focus of x^2=4y

Q: Consider the parabola y = -x +4x + 9 and the line y=2x + 1. Solve for the x-coordinates at their…

A: x - coordinates of the point of intersection = ?

Q: 5x – 8x? and the here is a line through the origin that divides the region bounded by the parabola y…

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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: A parabolic arch has an equation of 7x + y- 260 0. Find the maximum height of the arch. units

A: The equation of parabolic arch is: 7x2+y-260=0

Q: If a person shoots a basketball overhand from a position 8 feet above the​ floor, then the path of…

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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: 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: 2. What is the value of y anytime a parabola intersects the x-axis?

A: It is known that the value of y on x-axis is always 0.

Q: A point moves on the parabola 10y = 5x² + 3 in such a way that when x = 6, the abscissa is…

A: Given: A point moves on the parabola 10y=5x2+3, when x=6 the abscissa is increasing at the rate of 2…

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 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: 3. Find the equation of the parabola with focus at F(3,2) and with the line x = -4 as directrix.

A: Topic- equation of parabola from focus ans directrix.

Q: Find constants a and b so that the minimum for the parabola f(x) = x2 + ax + b Occurs at the point…

A: The given parabola is : f(x)=x2+ax+b We need to find the values of a and b so that the minimum for…

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

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Q: The line y = mx +b intersects the parabola y = x^2 at points A and B. Find the coordinates of the…

A: The line y=mx+b intersects the parabola y=x2 at the pointsA and B.Let A=x1,x12 and B=x2,x22, where…

Q: Find the minimum distance from the point (4,2) to the parabola y2 = 8x.

A: We have to find the minimum distance from the point (4,2) to the parabola y2=8x.

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

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

A: We Can make it easier for you.

Q: 5. Find the equation of the hyperbola whose asymptotes are the straight lines x = 0 and y = 0 and…

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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: Find the y-intercept and any x-intercept(s) of the parabola with equation y = -(x + 7) + 16. If the…

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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: 13. Find the point on the parabola y* = 2x that is nearest the point (1, 4). %3D

A: As per our guidelines we can solve only one question or three sub-parts. To ask more please…

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 minimum distance between the point (5,1) and the parabola y=-x2 ?.

A: Find the minimum distance between the point (5, 1) and the parabola y = -x2?

Q: A parabola Is opening downward, always having a length of latus rectum equal to 4. The vertex of…

A: vertical assymptotes are vertical lines ( parallel to y-axis ) which touches the curve at infinity…

Q: Find a parabola with equation y=ax^2+bx+c that has slope 4 at x = 1, slope -8 at x = -1, and passes…

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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: 10. focus of parabola X-12y is 1- (6,0)

A: Here we have to find the focus of the parabola,  The given parabola is X2=12y .............. (1)

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: What point on the parabola y = 1-x is closest to the point (1,1)? The point on the parabola y = 1-x2…

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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: A point moves on the parabola 10y = 5x² + 3 in such a way that when x = 6, the abscissa is…

A: To find the increasing rate of ordinate at x=6, differentiate 10y=5x2+3 with respect to time, t,…

Q: A parabola is opening downward, always having a length of latus rectum equal to 4. The vertex of…

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Q: Find two values of d such that the line 2x + y = d is tangent to the ellipse 4x2 + y2 = 81. Find the…

A: Given,           The line 2x + y = d is tangent to the ellipse 4x2 + y2 = 81.We know that,y = mx + c…

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: Find the shortest distance of the point (6,3) to the parabola y=x2

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