1. Find the equations of the tangent and normal lines to the following curves at the point indicated. a) y=2x -3x+1: P(-1, 6) b) y=x-2x-1; P(2, 3) e) y=2+x: R6.-4) x':

Q: Find the condition that the line ax+by=1 may be a normal to the curve an-1y=xn

A: To find the condition of line ax + by = 1 which is normal to the curve a^(n-1) y = x^n

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 the equations of the tangent and normal line to the following curves at an indicated points:…

A: 1). Given curve is y=2x2-5. To find the equations of the tangent and normal line at point 2,3.…

Q: What is the equation of the tangent line and the normal line to y = x2 – 4x + 2 at (4,2)…

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

A:

Q: Find the slope of the tangent line to the graph at the given point. (x² + y2)² = 4x²y, (-1, 1)…

A: Given equation :x2+y2=4x2ywe have to find the slope of the tangent line at -1.1

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: 1. Find the set of points in the curve y = where the tangent lines are horizontal. r²+1

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

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

A:

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: B. Find the slope and the equation of the tangent line to the curve 1. y = 4 - 3x at (- 1, 1) 2. y…

A: We need to find the slope and the equation of the tangent line tothe following curve:3. y=3x2+2 at…

Q: Find equations of the tangent lines to the curve y = x-1/x+1 that are parallel to the line x − 2y =…

A: Given,        The equations of the tangent lines to the curve y=x-1x+1 that are parallel to the…

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: Find equations for the lines that are tangent and normal to the curve at the point (1,1).. x³ + y² =…

A:

Q: Find an equation of the tangent line to the given curve at the specified point. 5x y = X + 3' (2, 2)…

A:

Q: Find an equation of the tangent line at the given point. xy + x2y2 = 6, (2, 1)

A: We first find dy/dx at x=2, y=1

Q: Verify that (4,1) on the curve x + /xy = 6 and find the lines that are tangent and normal to the…

A: Given that, the curve is x+xy=6. Differentiate the curve x+xy=6 with respect to x as follows,…

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 an equation for the tangent line to the curve y = 4 at the point (3,16). X - 1 Oy - 16 = -3(x -…

A:

Q: #2. Find the slope of the tangent line to the curve at the indicated point: (a) x² +x°y² – y° =13 at…

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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: Find equations of the tangent lines to the curve х — 1 x + 1 that are parallel to the line x – 2y =…

A:

Q: Find the equation of the tangent line to the curve at the given point. y = /2x +1, (4, 3)

A: To find the slope, we find dy/dx at (4, 3) At (4, 3):

Q: find an equation of the tangent line at the given point. xy + x2y2 = 6, (2, 1)

A: Our Aim is to find an equation of the tangent line of the given pointxy+x2y2=6 -(i) at…

Q: 4. Find the equation to the tangent line to the curve -3 %3D at the point (x, y) = (1,2).

A:

Q: 1. Find the equations of the tangent line and the normal line to the curve y = V4x – 3 at the point…

A: 3) Given curve : y=4x-3 To find: The equaton of the tangent line and normal line to the curve y=4x-3…

Q: 1. Find equations of the tangent line and normal line to the following curves: 2x a) y = at the…

A: a) Given curve is y=2xx2+1 Given point is 1,1. Differentiating the given curve with respect to x,…

Q: What is the equation of the line tangent to curve defined by x + 4y² = 17 at the point (1, -2)?…

A: equation of line tangent

Q: Find the equation of the tangent and normal line using the stipulated conditions   1.) y = x2 - 5x…

A: Given the equation is y = x2 - 5x The point of intersection line y=6 The equation of the tangent is…

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

A:

Q: Find an equation of the tangent line to the curve y = 3 arccos (1,4 π). Select the correct answer.…

A: Find an equation of the tangent line to the curve y= 3cos-1(x/2) at the point (1,4π) .

Q: 1. Find the equations of tangent and normal lines to the curve whose equation y2 – 6x2 + 4y + 19 = 0…

A:

Q: 2- Find the equation of the tangents to curve given parametrically by Y= sin(x²)+1 at…

A:

Q: 19. Find the lines that are (a) tangent and (b) normal to the curve y = x' at the point (1, 1).

A: Given curve: y=x3

Q: Find equations of the tangent line and normal line to the curve at the given point. y = x* + 9e*,…

A: The given equation of the curve is: y=x4+9ex.   We have to find  the equation of the tangent line…

Q: Find the equations of the tangent and normal lines to the graph of  (x^2 + y^2)^3 = 8x^2y^2 at…

A:

Q: 1. Find the set of points in the curve y = A where the tangent lines are horizontal.

A: we have to find the set of points in the curve y=4xx2+1 where the tangent lines are horizontal. as…

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

A:

Q: 7. What is the equation of the tangent line and the normal line to y = x² – 4x + 2 at (4,2)…

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the…

Q: 16. Find the equations of the tangent and normal lines to the curve 16x* + y* = 32 at its points of…

A:

Q: 2. Consider the curve given by 3y2 – 2x²y³ +2x +9 = 0. Write an equation for the tangent line to…

A: The given curve is, 3y2-2x2y3+2x+9=0 The slope of the tangent curve is given by dydx Determine the…

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: A) Determine the equation of the tangent line to the curve xsin(y) – x²cos(y) = 1 at the point (1,4)

A:

Q: Find an equation of the tangent line at the given point. 2x1/2 + 4y −1/2 = xy, (1, 4)

A: Given,

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…