Find the shortest distance from the point (1, 0) to the parabola y? by: (a) Eliminating the variable y (b) The Lagrange multiplier technique 4x Explain why procedure (a) fails to solve the problem, while procedure (b) does not fail.

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A: Given: The two corners of the auxiliary rectangle of a hyperbola are at -4,-7 and 0,0 and transverse…

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Q: What is the length of the latus rectum of a parabola having its vertex at the origin and focus at…

A: The length of latus rectum of parabola = 4a

Q: 7. Determine all values of a that will cause the parabola y=ax² +10x+1 to cross the x-axis at two…

A: 7) y=ax2+10x+1 ...................eq (1) For parabola to cross the x- axis put y=0 0=ax2+10x+1…

Q: What is the general equation of a parabola that opens upward with V(-1,2)?

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Q: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2.

A: Let's find differential equation.

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Q: The question is about Lagrange multipliers. Use the Lagrange multipler method to locate the point on…

A: The question is about Lagrange multipliers. Use the Lagrange multipler method to locate the point on…

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: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 9 −…

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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: What is the equation of the parabola with axis parallel to the x-axis, whose vertex is at (-1,7) and…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 9 –…

A: Given : A parabola, y = 9 - x²

Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 12 - x. What…

A: Given that the rectangle has its base on x- axis and its upper two vertices on parabola let us take…

Q: A point moves on the parabola y2 = 8 in such a way that the rate of change of the ordinate is always…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 6 –…

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

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

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

A: Given:- What is the equation of the directrix of the parabola having a vertex at (6,0), passing…

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Q: A rectangle is inscribed with its base on the xx-axis and its upper corners on the parabola y=2−x^2.…

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Q: Consider a parabola that intersects the x-axis at points (-1, 0) and (3, 0).

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Q: Find the equation of the parabola with vertex V (5,5) and directix the y-axis.

A: we have to find the equation of parabola

Q: what is the equation of a parabola with a vertex at (4, 8) and a directrix at y=5

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 8 -…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 4 –-…

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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: A rectangular object 25 m wide is to pass under a parabolic arch that has a width of 32 m at the…

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Q: A rectangle has its two lower corners on the xx-axis and its two upper corners on the parabola…

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Q: Sketch parabola y = x2 – 10x + 16 by plotting a few points to left and right of the vertex. (Find…

A: Given parabola y=x2-10x+16                  ....(1)

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

A: Given query is to find the equation of the paraola.

Q: If tangent lines to the hyperbola 9x2 − y2 = 36 intersect the y-axis at the point (0, 6), find the…

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Q: shortest distance from the point (0,6) to the parabola x² – 4y = 0.

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Q: What is the maximum area of a rectangle inscribed in the ellipse defined by x2/64 + y2/25 = 1? Enter…

A: Let the length and breadth of the rectangle as x, y respectively Area of rectangle = xy Now…

Q: 1. Determine the equation of the parabola whose vertex is at the point (-1, –1) and whose directrix…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 1-².…

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Q: A rectangle is constructed with its base on the​ x-axis and two of its vertices on the parabola…

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Q: What point on the parabola y = 3- x² is closest to the point (3,3)? The point on the parabola y = 3…

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Q: 3. Find the dimensions and area of the largest rectangle having its two lower corners on the x- axis…

A: The given problem is solved below in detail.

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

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Q: What point on the parabola y = 5-x is closest to the point (5,5)? The point on the parabola y = 5- x…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 9 − x…

A: Given A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y =…

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 4 -…

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Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 12 - x2. What…

A: First draw the situation roughly

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 6 –…

A:

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 9 –…

A:

Q: A rectangle is to be inscribed in the ellipse described by x? + = 1. What should the dimensions of…

A: Given,  The equation of the ellipse x2 + y29 = 1  We have to find the dimension of rectangle with…