2. Find the equation of the horizontal asympto

Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y,   (−7, 49/2)

A: The objective is to find the equation of the tangent line to the parabola at the given point.

Q: 3. Find the equation of the tangent to the graph y = xvx-1 at ( 5, 10).

A: “Since you have asked multiple questions, we will solve the first question for you. If you want…

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: Show that the equation of the tangent line to the hyperbola                        x2/a2 − y2/b2 = 1…

A: Given Data The equation of the hyperbola is x²/ a²- y²/ b²=1. The points are (x0,y0).…

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: Find an equation of the tangent line to the graph at the given point. (y - 3)2 = 4(x- 5), (9, 7) %3D…

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Q: Find the points on the curve xy2 = 54 nearest the origin.

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Q: Find the points on the ellipse 2x + 4y = 1 where f(x.y) = xy has its extreme values.

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Q: The horizontal asymptotes of the curve 3x y = (x4 + 1)'/4 are given by %3D Y1 = and Y2 = where y1 >…

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Q: Find the points on the curve x^2y = 2 nearest the origin.

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Q: Find the point on the curve y2 = ;(x+1) which is nearest the origin.

A: We have to find the point on the curve y2=52x+1 which is nearest the origin.

Q: 2. Find the slope of parabola y = ²+3 at any point on the curve.

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: Let P(t) be the population of a bacteria culture after t days and suppose that P(t) has the line y =…

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Q: Find the asymptotes of the cissoid of Diocles defined by the equationy2(2a−x)=x3,a>0.

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Q: Find an equation of the tangent line to the graph at the given point. (y - 3)² = 4(x - 5), (6,5) ||…

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Q: How do I find the equation of the tangent line for this ellipse at the point (5/2,1). (x-1)^2/9  +…

A: Follow the steps.

Q: Question #2 Determine the value of so that the average rate of change of the parabola y = -2x + bx…

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Q: Find the asymptotes of the curve y3+x2y+2xy2-y+1=0.

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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 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: How can we find the horizontal and vertical asymptotes of the curve?

A: We find the horizontal and vertical asymptotes of the curve

Q: Find the point on the curve y2 =;(x + 1) which is nearest the origin.

A: If (x, y) is any point on the curve nearest the origin then the square of its distance from the…

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: Find the point on the curve y2 =(x+1) which is nearest the origin.

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Q: Find the point on the curve Y = √x closest to the point (3,3)

A: Given the curve is  y=x So the coordinates of any point in curve is given by x,x The distance…

Q: ind the equations of the tangent line to the ellipse x² + 4y² + z² = 9, x = 2 at the point (2, -1,…

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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: 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: 7. For whit value of b will the line y =- y 3x +4x -1? 2x+ b be tangent to the parabola

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Q: 9) Find the slope of the tangent line to the hyperbola defined by the equation y2 - x2 = 7 at the…

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Q: Give the equation of the tangent which passes through the point with the coordinate x=2 of the…

A: Equation of tangent problem.....

Q: Find equations for two lines through the origin that are tangent to the ellipse x2 – 8x + y² + 3 =…

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Q: The slope of the tangent line to the parabola y = 3x + 3 + 4 at the point (5, 94) is: 33 The…

A: Equation of parabola y=3x2+3x+4 The slope of the parabola at any point is calculated as  dydx=6x+3…

Q: Find the horizontal and vertical asymptotes of the curve. 2ex y = ex – 6

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Q: Find the lines tangent to the ellipse x2/4 + y2/9=1 that contain the point (4, 0).

A: We at first consider the equation of tangent  to x2/4 + y2 /9=1 with slope m. Then we find the value…

Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y,  (−9,81/2)

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Q: A particle travels along the parabola y = ax^2 + x + b. At what point do its abscissa and ordinate…

A: Given: y=ax2+x+b

Q: Find the closest point to the point (2,0) on the y = x curve.

A: To find the closest point to the point (2,0) on curve y=x

Q: Find the length of the arc of the parabola y²=4x from the vertex to a point where x=4.

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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: Show that the equation of the tangent line to the hyperbola x2/a2 − y2/b2 = 1 at (x0, y0) is x0x/a2…

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Q: 7. Find the member of the curve whose slope at any point is 2e¹x and passes through the point (0, 1)

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Q: Find the equation of the line tangent to the ellipse x^2 - xy + 2y^2 - 4x + 2y + 2 = 0 if the…

A: given equation of ellipse x2-xy+2y2-4x+2y+2=0 and a line  4y-x+2=0 to find equation of line tangent…

Q: 5. Find the point on the parabola y=-x+3x+4 where the slope of the tangent line is 5.

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Q: Find the arclength of y = 4x2 - 4 where x is greater than or equal to 0 and less than or equal to 4

A: Concept Used: The arc length of the function is the length of the curve y=fx on the interval a,b is…

Q: Find an equation of the tangent line to the graph at the given point. (y - 3)2 = 4(x – 5), (9, -1)…

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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: Find the points on the curve x2y = 2 nearest the origin.

A: The curve is x2y=2 Let x1,y1 and x2,y2 be two points, distance betwwen these points is x2-x12+y2-y12