Q: A curve passing through the point (1,1)has the property that the perpendi cular distance of the normal at any point P on the curve from the origin is equal to the distance of P from x - axis.Determine the equation of the curve.

Q: Find the Equation of the tangent line and the normal line for the following function: x* - xy + y =…

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Q: 7. For the curve y = x2 + x, at what point does the normal line at (0,0) intersect the tangent line…

A: Find the slope of the tangent at (0,0): m=dydx=2x+1=20+1=1

Q: Find the equation of a NORMAL LINE in SLOPE-INTERCEPT FORM to the given cu below f (æ) = (x² + 1)*…

A: Note: The normal line is defined as the line that is perpendicular to the tangent line at the point…

Q: Find the equation of the normal at (1,2) for the function 2x - 3xy+ y +x+2y+12%3D0.

A: Equation of normal for a  curve at a point (a,b) is given by, y-b = m(x-a) Where m is the slope of…

Q: 5.Find the equation of tangent and equation of normal to the curve, 1 (3x - 1) 3xy = 5-8y' at the…

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Q: (b) Find the equation of the normal to the curve 4x +2y 10xy at the point (1.2). %3D

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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 equation of the normal to the curve y(x+1) = x²+2y at x = -1

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Q: at x = 2 2. Find the equation of the normal line to y

A: The solution of the problem is given in the next steps.

Q: 2. Find the equation of the curve so drawn that every połnt on it is equidistant from the origin and…

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Q: find an equation for the tangent line and the normal line to the curve y = x sqrt x^2+1 for the…

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Q: b) Find the equation of the normal line to the curve y = 1 – x³ at x = -1. Sketch the graph.

A: given:  y=1-x3           1 Differentiating (1) wrt x dydx=-3x2 At x=-1, dydx=-3 Also, At x=-1, from…

Q: Identify the equation of the normal to the tangent line at the point (3,3) for the equation xy-9=D0…

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Q: Find the point(s) on the graph of y = (x2 – 168)e × where the tangent line is horizontal. Identify…

A: Given y=x2-168ex Consider, fx=x2-168ex To find the points on the graph where the tangent line is…

Q: (b) Find the equation of the normal to the curve 5x² +4y = 12xy at the point(2,1).

A: Given: 5x2+4y3=12xy, at point2,1 For finding equation of normal at point2,1, we need to find slope…

Q: Find the normal to the curve y 1 x2 at the point (3, -8). y=(x/3)-(3/2) O y=(x/2)+(3/2) O…

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Q: Find all points​ (x,y) on the graph of y=x/(x−1) with tangent lines perpendicular to the line y=x−8.

A: The given function for the tangent is, Differentiate the above expression to get the slope of the…

Q: The function f is defined forx>0 and is such that f'(x) 2x -. The curve y = f(x) passes through the…

A: Follow the steps.

Q: Find the tangent and normal of y + (x+y)^1/2 =x at point (3,1)

A: To find the equation of tangent, first, find the slope of the tangent. The slope of the tangent is…

Q: Find the equation of the normal line to the curve y=arccot1x at x=1.

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Q: Find the equation of the tangent and normal line at the point indicated. Sketch the curve. у %3 х3 —…

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Q: 4. What is the equation of the normal line to the curve 4x2 – 9y2 = 1 at point (3,2) ? a. y =x- 4 5.…

A: Slope of the Normal Line to the graph of f(x) is  -1f'(x). Equation of the line : y-y1=mx-x1 where,…

Q: Consider the following. y = x6/5, (1, 1) Find an equation of the tangent line. y = Find an equation…

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Q: Find the equation of the normal to the curve y = x?e4* at the point x

A: We have to find Normal to the given curve.

Q: 11. At what point(s) of the curve xy = (1 – x – y)? is the tangent line parallel to the x-axis? Give…

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Q: A curve is given by xcos('pi'xy)=x+y+1. Find the tangent -and normalline at the point (0,-1).

A: Given x cosπxy=x+y+1

Q: 2л Find the equation of the normal to the curve y = sin 3x at the point x = Select one: O y = x+ -…

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Q: What is the equation of the normal to the curve x+y = 25 at (4,3)? Select the correct response:…

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Q: For the function f(x) = x² – 4 at the point (4, 12), find: a. the slope of the curve using the…

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Q: 4. Find the equation/s of the normal line of slope 2 to the ellipse x² + 2y² = 3. 5. At what point…

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Q: 23. Find the normal to the curve x2 + y² = 25 at (4,3). %3D

A: Find the normal to the curve

Q: What is the equation of the normal line to the curve y = cos æ at the point (6,0) ... A y = -x +; 2…

A: Given:- y = cos(x)  To find:- Equation of normal line on given curve at point (π/2 , 0)

Q: The curve y : in (3x - K) crosses the at and the equalion of the at this point Find the value of K…

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Q: d) Determine the equation of the normal line to the graph of the function y+z*v = z sin(u") + vye"…

A: According to the given information, it is required to find the equation of normal line of the given…

Q: Find the equations of the tangent and the normal at the point (2,2) at x² – 2xy + y² +2x + y - 6 = 0

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Q: Given that f (x) = Vx2 +1 Determine the equation of the tangent at x = 1. Determine the equation of…

A: The given curve is: f(x)=xx2+1

Q: What is the slope of the normal ine to the curve y=In(xª+1) at x=1, -2 -1/2 1/2 D) 2

A: Product of slope of the tangent and normal line 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: at x= - 2 Given : x-Xy + 2y -3 = 0

A: Given : The equation of curve x2 - xy + 2y - 3 = 0  To find the equation of the tangent and the…

Q: 5. What is the slope of the tangent line to the curvex²e-2x - y = 0 at the point (-1, e2²)?a. a. 4…

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Q: Q-2- Find the eAuation of the tangent line.and the normal line for the fallowing function X = 0-…

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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: The slope of the normal line to the tangent line of 1 is -1 f(x) = (sin x)² at x = V2 :Select one V2…

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Q: Q-2- Find the equation of the tangent line. and the normal line fer the fallowing function X = Qa…

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Q: d the exact equation of the normal to y=e2x at the point where x=

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Q: Q4) Find the equation of the normal to the curve [y+x(1+y)-4] at point (2,1).

A: Given equation is y2+x1+y-4=0 and we have to find the equation of normal to the…