The family of curves orthogonal to ye2x = c is the family of curves whose general equation is?

Q: Determine a, b, c and d so that the curve y = ax³ + bx² + cx+d₂ pass through (-1, -1) and have at…

A: To Determine: Value of a, b, c and d so that curve y = a x3 + b x2 + cx + d

Q: Area of a regim enilosed is by Curves y= 12 and

A: To find the area enclosed by the given two equations

Q: Find an equation of the tangent line to the curve 2(z² + y°)² = 25(æ² – y³) (a lemniscate) at the…

A:

Q: Find the exact length of the curve.10. 36y 2 = (x2 – 4)3, 2 ≤ x ≤ 3, y ≥ 0

A: Given :                36 y2  =  ( x2 - 4)3  To find :                  The exact length of the…

Q: 4 Find all the points on the curve x2 + xy + y? = 3 where the tangent to the curve is a vertical…

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Q: Please help me find the length of the curve

A: We\'ll use arc length formula with a=pi/2, b=2pi/3.

Q: Find the equation of the family of curves at every point of which the tangent line has a slope of…

A: We have to find the equation of the family of curves at every point of which the  tangent line has a…

Q: Find the exact length of the curve. y = 7+ cosh (2x), 0 ≤ x ≤ 4 1 2

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Q: Find the ponits on the curve 9y2 =x3 where normal to the curve makes equal intercepts with axes

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Q: Consider the curve defined by the equation y3+xy+2=0.  Show that there are no points on this curve…

A: Consider the given curve define by the equation:

Q: Consider the curve defined by the equation y³ + xy + 2 = 0. Show that there are no points on this…

A: Given Equation of curve   y3+xy+2=0  ---(1)

Q: Find an equation of the tangent line at the point specified. y = excos2 x, x = π/4

A: Given curve is y=excos2x. To find the equation of the tangent line at the point x=π4. Solution: The…

Q: Find the equation of tangent to the circle x + y = 25 at the point (3, –4)

A: Equation of the tangent line

Q: Find the equation of the tangent line to the curve at the given point. y = 9x - 8Vx, (1, 1) %3D

A:

Q: find equation for the lines that are tangent andnormal to the curve at the given point. ex + y2 = 2,…

A: Given: Equation of curve ex+y2=2 and the point 0,1, To find: Equation of tangent and normal line to…

Q: At what point is the tangent line to the curve y3=2x2 perpendicular to the line x+2y-2=0? P= (?,?)

A: We have to find the point

Q: Suppose a curve is defined by the equati on y2 = x*(2- x). What is the equation of the line tangent…

A: Given curve

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: Find the tangent and normal line to the curve at the specified condition. 12x2 - 20y2 = 55 parallel…

A: Given that the curve is 12x2-20y2=55 and the required tangent and normal line is parallel to the…

Q: Plot the curve x³ + y3 = 6xy together with the tangent to the curve at the point

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Q: Find the exact length of the curve. 1 y = 1 + cosh(8x), 0 ≤ x ≤ 1 8

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Q: 1. y = 2x2-5 at ( 2, 3) %3D

A:

Q: The family of curves orthogonal to x2 + 4y2 = c2 has the general equation 04. %3D

A:

Q: Find eacation for tangent to curve ンt (-3, 2d) +4) 4X

A:

Q: Find the ponits on the curve 9y2=x3 where normal to the curve makes equal intercepts with axes

A:

Q: Two stations, located at M(1.5, 0) and N(1.5, 0) (units are in km), simultaneously send sound…

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Q: The slope of the tangent line to the curve y at the point ( 5, is: The equation of this tangent line…

A: Given curve is : y=3x To find the slope of tangent at the point 5,35 and equation of tangent in the…

Q: Find an equation of the tangent line to the curve atthe given point.

A:

Q: Find the slope of the tangent line to the graph r=2sin(0) at the point V3, 3 11.

A: We have to find

Q: At what point is the tangent line to the curve y = 2x perpendicular to the line x – - 2y – 8 = 0? -…

A:

Q: A curve like Y = is called a serpentine. 1+2x2 3 n equation of the tangent line to this curve at the…

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Q: Find the equations of the tangent lines to the circle (x + 2)² + (y + 2)² = 25 at the two points…

A: At x=2; (2+2)2+(y+2)2=25 16+(y+2)2=25 (y+2)2=9 y+2=±3y = 1 or -5Therefore two points at which…

Q: Use the guideline of this section to sketch the curve 1. y = 1 + 1/x + 1/(x ^ 2)

A: To Sketch: y=1+1x+1x2 Explanation: (a). Domain and Range y=1+1x+1x2is defined everywhere except…

Q: Find an equation of the tangent line to the curve x^(2/3)+y^(2/3)=13 at the point (−27,−8).

A: Given:

Q: At what point is the tangent line to the curve y³ : = 6x² perpendicular to the line 2x + y = 2 = 0?…

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Q: Find the exact length of the curve. y = In(sec(x)), Osxs- 6

A:

Q: Find the equation of the line that is tangent to the curve y =-3e* at x = In 2. %3D

A:

Q: Find the length of the curve for 12x = 4y³ + 3y-¹ where 1 ≤ y ≤ 3 Enter your answer in exact form.…

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Q: (a) Find the equation of the tangent plane to the graph of : = (1,-1,5). + ) +4 at

A:

Q: Find the equation of the tangent line to the curve y=x-6cos(x) at the point (0,-6)

A: We have to find equation of tangent line to the curve y=x-6cos(x) at the point (0,-6)  Now first we…

Q: Find the exact length of the curve. 36y² = (x²-4)³, 4≤x≤6, y 20

A:

Q: Find an equation of the tangent to the curve r + ry + y² = 3 at (-2, 1). %3|

A: First find the slope of the tangent with the help of derivative of the curve than write the equation…

Q: 12)What is the slope at (1,2) for curve define by xy^2=4?

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Q: . Determine the points where the curve 6x+ 4y-y=6 has a vertical tangent line. p. Does the curve…

A:

Q: Find the exact length of the curve. y = 9 + ¹ cosh (8x), 0≤x≤7

A: The curve y=9+18cosh8x, 0≤x≤7

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: The curve defined by the equation x^2+y^2=(2x^2+2y^2-x)^2 is called a cardioid. Find the equation of…

A: consider the given equation, x2+y2=2x2+2y2-x2 Use implicit differentiation method and differentiate…