Find the point on the parabola * +y“ that is closest to the point (0, -3). =

Q: At what point of the parabola is the tangent line parallel to 7x+y-2=0? y=2x^2-3x+1

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Q: Find the slope and y-intercept of the line through the point (6,7) that cuts off the least area from…

A: The line passes through the point (6,7) that cuts off the least area from the first quadrant.

Q: There is a line through the origin that divides the region bounded by the parabola y = 7x X-axis…

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Q: What is the equation of the line tangent to the parabola y2=12x at point (2,2)

A: y2=12x  ⇒  4a=12                     a=3

Q: Find equations of both lines through the point (2, −30) that are tangent to the parabola y = x^2 -…

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Q: find all the points having an x-coordinate of 1 whose distance from the point (-3,-1) is 5.

A: Suppose that the points are of the form (x, y) where given that x = 1. So, the points are (1, y).

Q: Find the length of the arc of the curve 9y2 = 4x3 from the origin to the point (3,2v3).

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Q: The slope of the tangent line to the parabola y = 2x + 5x + 7 at the point (- 4, 19) is: 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…

A: To find a parabola with equation.

Q: What function should be used to minimize the distance between, y = 3x2, and the point (0, 2)?

A: y=3x2,  0, 2.

Q: Find a parabola with equation y = ax² + bx + c that has slope 4 at x = 1, slope -16 at x = -1, and…

A: We know slope of a curve y=f(x) is given by, dydx=f'(x)

Q: Use the derivative to find the vertex of parabola. y = -2x2 + 12x - 5

A: Given equation of parabola is y=-2x2+12x-5. To find the vertex using derivative. Solution: We know…

Q: Next There is a line through the origin that divides the region bounded by the parabola y = 4x –…

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Q: What is the maximum vertical distance between the line y =x +2and the parabola y =x2 for     -1 ≤ x…

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Q: Find the point on the curve y = sqrt x that is closest to thepoint (3,0)

A: Given curve y=x Let A(x,y)  be a point on the curve and let B(3, 0) So distance between A and B is…

Q: opens upward with vertex at (-12,-6) with directrix y=- 17

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Q: Find the equations of the tangents to the curve x = 6t2 + 2, y = 4t3 + 2 that pass through the point…

A: Given data:     The first equation is: x=6t2+2. The second equation is: y=4t3+2. The given point is:…

Q: 2 that also passes Write the equation for a quadratic function f(x) with roots at x = 7 and x =…

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Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – the…

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Q: Find a parabola with equation y = ax2 + bx + c that has slope 5 at x = 1, slope −11 at x = −1, and…

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Q: Find an equation of the tangent line to the parabola y − x2 - 8x + 9 at the point (3, -6).

A: The derivative of a curve at a point gives the slope of the tangent to the curve. It can be…

Q: The slope of the tangent line to the parabola y=4x2+2x+6y=4x2+2x+6 at the point (-3,36) is: ?

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Q: The slope of the tangent line to the parabola y 4x + 7x + 5 at the point (0, 5) is: The equation of…

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Q: at the line x = 3. %3D

A: Find the volume of the solid generated by revolving the region between the parabola  x=y2+1 and the…

Q: Find the equation of the tangent line to the ellipse 25x2+ y2 = 109 at the point (2, 3

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Q: Find the slope and y-intercept of the line through the point (6,6) that cuts off the least area from…

A: Given : Point (6,6)

Q: There is a line through the origin that divides the region bounded by the parabola v X-axis into two…

A: Given- There is a line through the origin that divides the region bounded by the parabola y = 7x -…

Q: Find an equation of the tangent line to the parabola y=x2  -8x+9 at the point (3, -6)

A: Given :          y= x2-8x+9

Q: There is a line through the origin that divides the region bounded by the parabola y = 3x – 4x² and…

A: we have been given the parabola y=3x-4x2 to find the points put 3x-4x2=0⇒x(3-4x)=0⇒x=0, 34…

Q: The cubic y = ax3 + bx2 + cx + d that passes through the points (-1, -10) and (1, -4) and tangent to…

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Q: Find the equation of the line through the point (2, 5) that cuts off the least area from the first…

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Q: find the point p on the line y=5x that is closest to the point (78,0). what is the least distance…

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Q: Find the slope of the tangent line to the parabola y = x2 at the point (2, 4) by analyzing the…

A: We have to find the slope of tangent line to the given parabola y=x2 at the point 2, 4 by analyzing…

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x - 5x² and…

A: Given that equation of parabola y=4x-5x2let ,equation of line y=mx   where slope=m which is devide…

Q: The line y = 2x - 9 is tangent to the parabola y = x'2 + ax + b at the point (4,-1). What are the…

A: Given y=2x-9 is tangent to y=x2+ax+b at (4,-1) So, y=x2+ax+b passes through (4,-1)Put x=4 and…

Q: Find the points on the curve y = 2x3 - 3x2 - 12x + 20 where the tangent line is a. perpendicular to…

A: Find the slope of the line y= 1- (x/24)

Q: There is a line through the origin that divides the region bounded by the parabola y = 5x – 7x² and…

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Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 3x2 and…

A: According to company rule, we can answer only first question and rest can be reposted.

Q: Write the equation of the circle of radius 5 that istangent to both axes and passes through the…

A: Write the equation of the circle of radius 5 that istangent to both axes and passes through the…

Q: What is the equation of tangent to the parabola y^2 = 2x + 8 at (4,4) ?

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Q: What are the coordinates of the points in the graph of y² – x² + 6x – 13 = 0 in which the tangent…

A: As we know that; The slope of the horizontal tangent line is zero or m=dydxPx0,y0=0 Given;…

Q: There is a line through the origin that divides the region bounded by the parabola y = 7x- 3x2 and…

A: Given the parabola : y=7x-3x2Let the line through the origin be : y=mx   , where m is the slope of…

Q: Find the point on the parabola y= X- + 4 whose tangent line is parallel with y = 3x -5

A: Let a point on the parabola is h,k. Now the slope of the tangent line is given by: m=dydxh,k Since,…

Q: There is a line through the origin that divides the region bounded by the parabola y = 7x – 2x and…

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Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 8x and…

A: There is a line through the origin that divides the region bounded by the parabola y=2x-8x2 and the…

Q: There is a line through the origin that divides the region bounded by the parabola y=8x−6x2 and the…

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Q: There is a line through the origin that divides the region bounded by the parabola y=7x-(2(x)^2) and…

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Q: Find the slope and y-intercept of the line through the point (2,7) that cuts off the least area from…

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Q: There is a line through the origin that divides the region bounded by the parabola y = 2x-6x and the…

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Q: What is the average distancebetween the parabola y = 30x(20 - x) and the x-axis on theinterval [0,…

A: The equation of parabola is given by y=30x20-x on [0, 20] The expression to evaluate the average of…