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

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 tangent to the parabola (x + 2y)² + 2x - y - 3 = 0, parallel to the line x - y = 1.

A: Consider the equation of the line x-y=1 ⇒y=x -1 Comparing with y=mx+c we get slope of line, m=1

Q: Find an equation of the normal line to the parabola y= x2 -5x +4that is parallel to the line  x-3y…

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Q: The slope of the tangent line to the parabola 2x + 4x + 5 at the point (3, 35) is: The equation of…

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Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y, (-5, ) 2у, %3D

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Q: Find an equation of the tangent line to the parabola y = x2 -1 at the point (2,3) y 4x-5 Oy - 4x - 9…

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Q: Show that the tangent lines at the points where the ellipse x² – xy + y² = 3 cross the x-axis are…

A: Explained below

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

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Q: How do you find the equation of the tangent line to the parabola for y = x2 − 3x − 1 at x = 4.

A: The equation of the given parabola is y=x2-3x-1. We have to find the equation of the tangent line to…

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

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Q: Find all points on the ellipse x2 - xy + y2 = 1 at which the tangent line is horizontal.

A: The given equation of ellipse is,

Q: 8. At what point of the parabola is the tangent line parallel to 7x+y-2=0? y = 2r-3x +1 O (1,0) O…

A: Here is the solution:

Q: Find an equation of the normal line to the parabola y = x – 9x + 5 that is parallel to the line x -…

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Q: The slope of the tangent line to the parabola y = 2x + 2x + 6 at the point (- 1, 6) is: The equation…

A: The slope of the tangent line to the parabola                      y = 2x2 + 2x + 6 at the point…

Q: The slope of the tangent line to the parabola y = 4x? + 7x + 2 at the point (– 4, 38) is: The…

A: Equation of parabola,  y = 4x2 + 7x + 2 Given point is (-4, 38)

Q: Find the parabola with equation y= ax2 +bx whose tangentline at (1, 1) has equation  y= 3x -2.

A: We have to find equation of parabola y=ax2+bx which has tangent y=3x-2 at 1,1 .

Q: Find an equation of the normal line to the parabola  y = x2 − 4x + 1  that is parallel to the line…

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Q: Find an equation of the normal line to the parabola y = x2 - 5x + 4 that is parallel to the line x -…

A: y=x2-5x+4 Differentiating with respect to x, we get dydx=2x-5 Now slope of the normal line is,…

Q: A baseball is launched into the outfield on a parabolictrajectory given by y = 0.01x(200 - x). Find…

A: Given ------(1)   The average value of a functionon an interval is given by ------ (2) From the…

Q: Find the parabola with equation  y = ax2 + bx  whose tangent line at  (1, −1)  has equation  y =…

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Q: Find point on the ellipse x^2+2y^2=1  where the tangent line has a slope of 1.

A: We know, slope of tangent line = dydx

Q: Find the orthogonal trajectories of the family of parabolas with vertices at the origin and foci on…

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Q: 3. Find the line normal to the ellipse at X=-1 y= 2+4x-x3

A: Given, y=2+4x-x3 At x= -1 y=2+4-1--13y=2-4+1y=-1 Now point -1,-1

Q: At what point of the parabola y = x² – 3x – 5 is the tangent line parallel to 3x - y = 3? O (-3,-5)…

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Q: Find the equation of the plane tangent to the graph of z + xyz = 33 at (1,2,3).

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Q: At what point does the normal to y = 3x – (5 + 4x) at (1, –6) intersect the parabola a second time?…

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Q: Where does the normal line to the parabola y= x- x2 at  the point (1, 0) intersect the parabola a…

A: Normal to a curve is a line which is perpendicular to the curve at its point of intersection with…

Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0,1) and is tangent to the…

A: Since, the parabola passes through (0,1) ,so,we substitute x=0, y=1 ,to get c=1

Q: Find an equation of the normal line to the parabola y = x2 – 8x + 4 that is parallel to the line x –…

A: Let the equation of the normal line in the slope-intercept form is, y=mx+c where m is the slower and…

Q: The x-coordinate of the point where the tangent line to the parabola y=2x^2 at x=1 intersects the…

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

A: Introduction: When a multivariable function is to be extremized under some constraints, we use the…

Q: Find the orthogonal trajectories of the family of parabolas through origin and foci on axis.

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Q: What is the equation of the normal line to the ellipse 8x^2 + 32y^2 = 256 at the point (4,2)?

A: the equation of the normal line to the ellipse can be found by differentiating the given equation…

Q: The slope of the tangent line to the parabola y 3x? + 2x + 3 at the point (– 5, 68) is: The equation…

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Q: Make the cubic y = ax3+bx2+cx+d pass through the points (0,-6), (1,-2) and be tangent to the line…

A: This is the simple question based on algebra and derivative which could be solved using the basic…

Q: Find x for which the line tangent to the parabola y = 4x − x^2 is horizontal

A: The objective is to find x for which the line tangent to the parabola y = 4x − x^2 is horizontal.

Q: Find the parabola with equation y = ax + bx whose tangent line at (1, 1) has equation y = 5x - 4.

A: ven parabola , y =ax2+bxtangent ,           y = 5x-4comparing with y = mx+c , slope of tangent m = 5

Q: Determine the equation of the normal line to the hyperbola x - 4y- = 9 at (5, 2). 8x + 5y – 50 = 0…

A: Given equation of hyperbola is  x2-4y2=9          ...(1) We have to find the equation of the normal…

Q: Find the equations of the tangent and normal to the parabola y² - 2x - 4y -1 = 0 at the point (-2,1)

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

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Q: Find an equation of the normal line to the parabola y = x2 - 8x + 9 that is parallel to the line x -…

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

A: Given: y=2x2-3+2x Point: 1,-3 Objective is to find the point where the normal to y=2x2-3+2x at…

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: What is the equation of the normal line to the ellipse 8x^2 + 32y^2 = 256 at the point (4,2)? O y =…

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Q: At what point of the parabola y=x -3x+5 is the tangent line parallel to the line 3x-y 2?

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Q: Determine the equation of the normal line to the hyperbola x2 – 4y2 = 9 at (5, 2).

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Q: Find the tangent line to the ellipse x^2+4y^2=8 parallel to the line x+2y=6.

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Q: 10. At what point on the parabola y = 3x² + 2x is the tangent line parallel to the line 10x – 2? y

A: Given,          The parabola y=3x2+2x is the tangent line parallel to the line y=10x-2.

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…