Find an equation of the normal line to y = x2 at the point (2, 4). (The normal line at a point is perpendicular to the tangent line at the point.) Where does this line intersect the parabola a second time?

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 an equation of the normal line to the parabola y= x2 -5x +4that is parallel to the line  x-3y…

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Q: Find equations of the tangent and normal line to the curve x? – xy – 3y2 = -4 at (1,2).

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Q: Find the tangent plane to the equation 5e*- öy at the point (12, 24, 5).

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Q: Find the equations of the tangent line in the given plane. Given: v = (3t - x)e-2t

A: Given function - v = 3t-xe-2tWe need to find ∂2v∂t∂x,Concept - We need to partially differentiate v…

Q: Find an equation of the tangent line and normal line to the curve at the given point. y = (2x)/(x2 +…

A: Given :          y=2xx2+1     1,1

Q: Show that the point (2, 4) lies on the curve x3 + y3 - 9xy = 0. Then find the tangent line and…

A: Given: f(x, y) = x3 + y3 - 9xy = 0 To find:  Equation of tangent and normal to the curve at point…

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: Find the equation of the tangent and the normal to the curve y=5x4 at the point (1,5)

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Q: 5. Find the equation of the tangent and normal line of 2x+1 y = at point (1,1). x+2

A: A detailed solution is given below     (As per our guidelines, we have to solve only one question)

Q: Find the equations of the tangent and the normal at the point indicated.   a2y = x3 at (a, a).

A: To find the equation of tangent and normal at the given point.

Q: (A) Find the equation of tangent and normal to the curve 2x2 + y = 9 at (-2, –1).

A: To find the equation of tangent and equation of normal at the given curve .

Q: Find equations of the tangent line and normal line to the curve at the given point. (1, 0.25) y=…

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Q: 1. Find the equation of the lines tangent and normal to the curve 3x?y2=4x2-4xy. at the point…

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: Find the equations of the tangent and the normal at the point indicated. y = 2 + 4x - x2 at x= -1

A: Given : The equation of the curve is y=2+4x-x2 at x=-1 Let m= the slope of the tangent line at x==-1…

Q: Find the equation of the tangent line and normal line to the graph of y = x-1 at the x+1 point where…

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Q: Find the tangent plane to the equation 4x2 + 3y2 – y at the point (-4,-1,68) Z =

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Q: Find the equation of the tangent plane to z at (-4,2).

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Q: Find the equations of the tangent and the normal of y = 3x2-2x+1 at point (1,2).

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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: Find an equation of the normal line to the parabola y = x2 - 5x + 4 that is parallel to the line x -…

A: y=x2-5x+4 Differentiating with respect to x, we get dydx=2x-5 Now slope of the normal line is,…

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 equation of the tangent line and the normal line at the p corresponding to the given value…

A: Let's find equation of tangent line and normal line.

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

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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 an equation of the normal line to the parabola y = x 2 - 5 x + 4 that is parallel to the line…

A: Given:       y=x2-5x+4 is parallel to the line x-3y=5.

Q: Find the equation of the tangent line and the normal line of the curves at given point 1. 4x? + 9x?…

A: The given equation,     4x2+9x2=25, 2,-1

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: Find the equation of the tangent and normal line at the point indicated. Sketch the curve. y = x –…

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Q: Find the slope of the curve and equations of the tangent and normal to the curve at the given point.…

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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: The equation of the line tangent to the curve at (−1,4)is x+y=3. What is the slope of the normal…

A: Product of slopes of two perpendicular lines is -1.

Q: y = x3 – 3x2 – 9x + 5 at x = 1

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Q: a) Find the equation of the tangent line to ƒ at (3, –27/17). y = -16.816x+48.198 b) Find the…

A: We find dy/dx using the quotient rule then we plug x=3 in it

Q: Find an equation of the tangent plane to the graph z = Væ + y³ nt (8, 2, 4).

A: We know that equation of tangent plane to the graph z=f(x,y) at point (a,b,c) is…

Q: Find an equation of the normal line to the curve y = x1/2 that is parallel to the line 2x + y = 1.

A: To determine a normal to the curve which is parallel to the given line

Q: Find the equation of normal to the curve y = 2x – 4x² +x- 6 at point (2,–4)

A: Given y=2x3-4x2+x-6 and point is P(2,-4)We need to find the slope i.e. y'dydx=ddx(2x3-4x2+x-6)We…

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

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

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Q: 2. Find atax

A: The symbol ∂2v∂t∂x is the symbol of partial differentiation. Differentiate the given function v…

Q: At what point of the parabola y=x -3x+5 is the tangent line parallel to the line 3x-y 2?

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Q: Find the equation of the tangent and normal line using the stipulated conditions   2.) x2 + 2y2 =…

A: The equation of tangent line is x2+2y2=9⇒x29+y292=1we have a=3 and b=92Since, we know that the…

Q: Find the equation of the line that is normal to the curve (y-x)2 = 2x + 4 at (6,2). %3D

A: Use equation of normal line

Q: (b) Find the equation of the normal to the curve 3x² +2y³ = 7xy at the point(2,1)

A: 3x2+2y3=7xy;(2,1)

Q: Find an equation of the tangent line and normal line to the curve at the given point. y = x* – 2e*,…

A: Given curve is y=x4-2ex. To find the equation of the tangent line and normal line to the curve at…

Q: Find the tangent plane to the equation 5e* бу at the point (12, 24, 5) Z =

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

A: Given,

Q: Find the equations of the tangent line and normal line to the curve y = (2 + x)e¬* at the given…

A: We will find out the required solution.