5. Straight lines with algebraic sum of the intercepts fixed as k. Am. (xy - yXy – 1) + ky' = 0.

Q: 1 find the length of the curve x = 7y* + y2, from y = 1 to 24 y = 2.

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Q: 4. Find the point(s) on the curve of y=,x+x+2for which the slope of the tangent line is zero. (5)

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Q: 8. Find all points on the graph of y = (x + 3)² at which the tangent line is parallel to the line…

A: The given graph is y = (x +3)2 To find the points on the graph at which tangent is parallel to the…

Q: 25. Find equations of all lines having slope −1 that are tangent to the curve y 1/(x − 1). = 1/4…

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Q: 1. Find the length of the curve y = 3 xi - () x , from x = 1 to x = 4.

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Q: 4. At what point on the graph of y =x2 is the tangent line parallel to the line 2x – 4y = 3?

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Q: 3. Find the points where tangent lines are vertical or horizontal: x³ + y³ = 6xy

A: Given:- x3+y3 = 6xy To find :- Points where tangent horizontal and vertical

Q: Find the exact length of the curve. y =  3 +1/2 Cosh 2x,   0≤ x ≤ 1

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Q: 8) Find the slope of the tangent line to the graph at the given point. (x² – y³)² = 4x²y - 3x -…

A: Consider the equation and the point

Q: 1. Find the are length of the curve x (+ 2)/2 from y=0 to y-1

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Q: 10. Find the length of the curve y = x/2 + 8 on the interval [0, 2]

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Q: The slope of the line tangent to the graph of y = In(x²) at x = e² is %3D

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Q: Find equations for the tangent lines to the graph at the given points 3xy + x2 = 4, (1, 1) and (4,…

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Q: 4. Find the equation of the tangent line and normal line that passes through the circle (x – 2)² +…

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Q: 7. Find the points on the curve y ve y = -x where the tangent line is parallel to the line y=

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: Find the distance from the point Q to the line ℓ.

A: Given: Q=0, 1, 0, l with equation xyz=111+t-203.

Q: Find the points on the graph of x^2+2x+4y^2=4+y where the tangent line is horizontal

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Q: 6. The slope of the line normal to the graph of y = 2 In(sec x) at x is 4

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Q: 9. Find the point (x, y) on the line y = 2x + 3 such that the distance from (x, y) to (1, 1) is as…

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Q: find equations for the lines that are tangent,and the lines that are normal, to the curve at the…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 3. Find the length of the curve y =x* +÷x¯² from x = 1 to x = 4

A: 3 Given function isfx=y=18x4+14x-2  from x=1 to x=4now we can writen as fx=x48+14x2 on 1,4The lenght…

Q: , If the curves yı = -x² + ax +b and y2 x² + cx - 2 have the common tangent line at the point P(1,2)…

A: Given information: There are two equations  are y1=-x2+ax+b, y2=x2+cx-2 have a common tangent line…

Q: Find the equations of tangent and normal lines of the curves at given points: y²-3xy - x = 0 at(2,8)

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Q: -1 Where on the curve y = (196 + x²)¯ does the tangent line have the greatest slope? NOTE: Enter the…

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Q: 2. Find the point on the curve y = VI thats is closest to the point (3,0)

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Q: 8. Find the point on the graph y = x³ where the tangent line is perpendicular to the line 3x +9y = 4

A: We have to find the point where tangent line is perpendicular to the line 3x+9y=4.

Q: 6. The slope of the line normal to the graph of y = 2 In(sec x) at x = is %3D

A: We need to find slope of normal line.

Q: 7.) Find the shortest distance between (4,2) and the curve y? = 8x.

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Q: Find an equation of the normal line to y = x2 at the point (2, 4). (The normal line at a point is…

A: y=x2 Differentiating with respect to x, we get dydx=2x Now slope of the tangent line at 2, 4 is,…

Q: (5) Find all the points on the curve y = 1/x where the tangent line is perpendicular to the line y =…

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Q: 1 - Find the equation of the tangent line to the curve y = 3 5 x2 +6x 2 11 at its point of…

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Q: 2. Find the equation of the tangent lines and the normal lines to the curve y = 2x² +3 at the point…

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Q: 4. Find the are length of the curve from y=1 to y-4

A: The given curve is x=18y4+14y-2 from y=1 to y=4

Q: Find all points (x, y) on the graph of y = with tangent lines perpendicular to the (x- 6) line y= 6x…

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Q: 1. Find the are length of the curve x = (y + 2)2 from y-0 to y=1

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: I Find the equations of tangent and normal lines of the curves at given points: a. x3 + y2 – 3xy = 0…

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Q: 1. find an equation of the line tangent to y = x-3 at point (O,-) %3D

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Q: 5. Find the length of the curve x = +22 from y =0 to y=3.

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Q: 9. Find the point on the graph of y = x² where the tangent line is parallel to the line 3x – 4y = 4.

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Q: 17. The line with equation y = 2x b where bis a constant, passes through the point (3, 6). What is…

A: When a line passes through a point then the coordinate  values of the point must satisfy the…

Q: 16. XZ is tangent to circle O at point X and XT is a secant line. If the m <TXZ = 69, find the m XT.…

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Q: 11. Find the distance between the point (1,0,-1) and the line x = 5 – t, y = 3 t, z = 1 + 2 t.

A: 11) The direction ratio of the lines  = -1,3,2 The direction ration of the point (1,0,-1) and the…

Q: Find all points (x, y) on the graph of y with tangent lines perpendicular to the line y = 4x - 5. (x…

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Q: 7-The tangent of the curve x^2+y^2- 2XY3D0 at the point (1,1), is *

A: Given,           The curve is x2+y2-2xy=0 at the point 1,1.

Q: 7. Find all points (x, y) where the curve y = xe has a horizontal tangent line. 2

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Q: 4) Find the equation of tangent I point line to the circle below at point (1,-3). * x² + y² – 2x –…

A: Consider the given equation of the circle, x2+y2-2x-4y-20=0 The equation of the tangent line passing…

Q: 10. Find the length of the curve y = x/2 + 8 on the interval (0, 2]

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