The equation of the parabola y' = 4ax is in the standard form. FALSE O TRUE

Q: Find the points on the ellipse x2+2y2=1, where f(x,y)=xy has its extreme values.

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Q: What point on the parabola y=3−x2 is closest to the point ​(3​,3​)?

A: Basic differentiation is required.

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: Finally, determine a. The parabola passes through the point (0, 5). Substitute the values of x and y…

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Q: At what point does the line normal to the graph of y=5−4x+4x2 at (1,5) intersect the parabola a…

A: The given function is- y=5-4x+4x2.................1 Differentiating the above expression w.r.t. x-…

Q: At what point does the normal to y = 2 + 2x + 2x² at (1,6) intersect the parabola a second time?

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Q: 1. Find the equation for the parabola that has its vertex at the origin and has directrix at y = 25…

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Q: 15. x2 – 8x + 2y + 10 = 0 Equation:

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Q: At what point does the normal to y=4x2−(2+3x)y=4x2−(2+3x) at (1,−1)(1,−1) intersect the parabola a…

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Q: Find the equation of the line tangent to the hyperbola x + 2xy - y + x = 5 at the point (3,7)

A: Given,            x2+2xy -y2+x =5 and point (3,7)

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

A: equation of parabola:-

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: Find an equation of the tangent line to the hyperbola y=3/x at the point (3,1)

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Q: transform into standard form of hyperbola x^2-y^2+6x-4y-4=0

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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: 3- The parabola y= ax'+bx+e, mean that the equation y ax' is . .........

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Q: Find the slope of the line tangent to the conic section 25 (x+3), (y+2)² = 1 at (3,8). 36

A: We find the slope of tangent to the given conic with the help of calculus .

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 point on the hyperbola xy = 8 that is closest to the point (3,0)

A: Given: xy=8 so, y=8x now any point of given hyperbola can be written as x,8x so, let's that point on…

Q: Find the equation of the tangent to the hyperbola x2 - 4y2 = 9 at (5, 2).

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Q: find the equation of the tangent line through the point (2,-2) to the hyperbola x2-y2=16.

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Q: Find the equation for the parabola that has its vertex at the 1 origin and has directrix at y 41…

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Q: 1 Find the equation for the parabola that has its vertex at the origin and has directrix at y 27…

A: Given: y=-127.

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

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Q: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2 Ans: 2xy" - 4yy"…

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Q: Find the equation of the line tangent to the hyperbola x2 −y2 =16 at (5,3).   Give your answer in…

A: The line is tangent to the given hyperbola at (5,3).Tangent line is a straight line.Therefore, the…

Q: Show that the “conic section” with equation x2 − 4x + y2 + 5 = 0has no points.

A: Equations for conic sections are obtained as the locus of points following one or a set of…

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

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Q: Show that the line b2xx1 - a2yy1 - a2b2 = 0 is tangent to the hyperbola b2x2 - a2y2 - a2b2 = 0 at…

A: Find dy/dx.Then find dy/dx at the point (x1,y1) by plugging x=x1 and y=y1

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

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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 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: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2. Ans: 2xy" -…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find an equation of the tangent line to the hyperbola defined by (5x^2)+(4xy)−(2y^2)−4x=195 at the…

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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: Find the equations of the normal and the tangent to the hyperbola xy + 2x - 5y-2= 0 at the point (3,…

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Q: Find the points on the ellipse 2x +y 1 where f(x,y)= xy has its extreme values. %3D

A: Solution:- Here we have to find the extreme value of  f(x,y)=xy subject to constraint…

Q: Identify the type of conic section from the equation: y^2 - 4y - x^2 6x =12

A: We have been given the equation  y2-4y-x2+6x=12

Q: If a is greater than or equal to zero the equation of the parabola is of the form?

A: Parabola is a three dimensional curve, where any point is at fix distance from the point called…

Q: 3- The parabola y= ax'+bx+c, mean that the cquation y = ax is .........

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

Q: 3. Find equations of both the tangent lines to the ellipse x²+4y?=36 that pass through the point…

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Q: Determine the equation of the normal line to the hyperbola x^2 - 4y^2 = 9 at (5,2)

A: We have to find equation of normal

Q: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex…

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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 equation for the parabola that has its vertex at the origin and has directrix atI = 27…

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

A: Given that a person shoots a basketball overhand from a position 8 feet above the​floor, then the…

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

A: Solution is here