Consider the curve described by the equation 2y2-x2 = 4y. Then verify that the point (4,-2) lies on this curve, and find y' at that point.

Q: Find an equation of the line tangent to the curve defined by z2 + 6ry +y = 32 at the point (2, 2).

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Q: the sloper of the curve 2y2=ax2+b at (1,-1) is -1.Find a,b

A: 1) Find dydx at the given points to find the value of 'a' . 2) Now satisfy the point (1,-1) to the…

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: Find the equation of the line tangent to the curve xy^3+xy=6 at the point (3,1). When the equation…

A: Firstly, we will find derivative And then we can solve for y'and we get

Q: Find an equation for the line in the xy-plane that is tangent and normal to the curve x³y² + y² = x…

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Q: consider the curve given by the equation x^3 - 2xy + y^3 = 0. Find the tangent line of this curve at…

A: Given equation is x3-2xy+y3=0..........(1) we have to find the tangent line of this curve at (1,1)

Q: Find the exact length of the curve. y = 1 - e-x ,    0≤   x ≤ 2

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Q: Find the equation of the tangent to the curve xy2 + y³ = 6x + 3y at (1,2)

A: The curve is given as x y2 + y3 = 6x + 3y, the objective is to find the equation of tangent line at…

Q: Find an equation of the line tangent to the curve defined by x2 + 6xy + y 32 at the point (2, 2).…

A: v

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: Find the equations of all tangent lines to the curve x² + 4y2 = 8 that pass through the %3D point…

A: The curve x2+4y2=8 that pass through the point (-4, 0). We have to find the equation of all tangent…

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: The curve y = x /( 1+ x2 ) is called a serpentine. Findan equation of the tangent line to this…

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Q: 2- Find the equation of the tangent line to the curve 7xSin(3y) + 5y = 7 at y = C

A: Given problem:- Find the equation of the tangent line to the curve 7xSin(3y) + 5y = 7 at y = 0

Q: x = e' and y = te %3D

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Q: Find the point on the Curve y rx that is closest to the point (2,0)

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Q: Find the equation of the tangent line to the curve y = x+5x* which is passing through point (1, 3):*…

A: Given : Curve  y = x + 5x2 Point 1,3   To find : The equation of the tangent line to the given…

Q: Given the curve y² = 5x – 1 at point ( 1,-2 ) , find the equation of tangent and normal to the…

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Q: Find the equation of the tangent to the curve x² +3y² = 6y at the point (1, ½)

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Q: Find the slope of the tangent line to the curve 3a2 – 3xy – 4y3 = 56 at the point (2, – 2).

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Q: Find the equation of the tangent line drawn to the curve y4−4x4−6xy=0 at the point M(1,2).

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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 equation of the tangent line at the given point on the curve. 2y - Vx = 4. (16,2) y =U

A: We need to find equation of tangent line.

Q: The equation of the tangent line to the curve y = x2 – 4x at the point where the curve crosses the…

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Q: Find the equation of the tangent line to the curve y=1-x² that is parallel to the line 2x-4y=8

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Q: At the given point, find the line that is tangent to the curve. 5x3y - n cos y = 6t, tangent at (1,…

A: 5x2y-πcosy=6π=ddx(5x2y-πcosy)=ddx(6π)=10xy+5x2y'+πy'siny=0=(5x2+πsiny)y'=-10xy y'=-10xy5x2+πsiny…

Q: Find the length of the curve y = 1 - e^-x, 0 <=x<=1.

A: The given curve is

Q: Consider the following curve: x? + y2 - 4x = 8xy² +92 An equation of the tangent line to the curve…

A: Our Aim is to find an equation of the tangent line to the curve given by:-x2+y2-4x=8xy2+92 -(i) at…

Q: Find the equation of the tangent line drawn to the curve y - 4x* – 6xy = 0 at the point (-1,3).…

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Q: Find the equation of the tangent line to the graph ofx^2 * y^2 + 3xy =18 at the point (-2, 3)

A: The given curve is: x2+y2+3xy=18 Differentiating both sides of the equation with respect to 'x', we…

Q: 4. Consider the curve given by r³ + y³ = 9ry. Find the equation of the tangent line at (4,2).

A: To find the slope of the tangent we need dydx at (4,2)…

Q: Find the equation of the tangent line at the point (−2,2) to the curve defined implicitly below. 4y2…

A: We have to  find tangent line to curve at given point at (-2,2).Cirve equation is given by:

Q: tangent

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

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Q: Find the equation of the tangent of the curve y=x^3+(3x)^(-1) at point (1,4)

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Q: Find c so that the line y = 4x + 3 is tangent to the curve y= x^2 + c?

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Q: The equation of the tangent line to the curve x² + y² = 64, at (9,-14) is

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Q: Find the equation of the tangent line to the curve at the given point. y = v2x + I, (4, 3)

A: →Slope, m = dydx→dax+bdx =12ax+b→Equation of straight line passing through (xo,yo) with slope m is…

Q: Consider the curve given by y2 + (1+x³)3 = xy + 8. Find the equation of the tangent line to the…

A: To find the equation of line tangent to the given curve at point (1,1)

Q: For the curve whose equation is given by x2 - 3xy + y2 - 4x + 2y +1 = 0, find the slope of the…

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Q: Find the equation of the line tangent to the curve xy3+xy=20 at the point (10,1). When the equation…

A: It is given that, the equation of the curve is xy3 + xy  = 20. Use implicit differentiation to…

Q: Consider the curve given by y2 + (1+x³)³ = xy + 10. Find the equation of the tangent line to the…

A: Considering the curve- y2+1+x33=xy+10 Firstly, find the slope of the curve. dy/dx is the slope of…

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: Find an equation of the tangent line to the curve y=3ex that is parallel to x-4y=1.

A: Given:Equation of a curve

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

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Q: Find the length of the curve of 8x = y² + 2y-² from y = 1 to y = 2.

A: Length

Q: Find the equation of the tangent line to the curve y = e' when it is paralel to 2r-y =7.

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