Show that the normal line at any point on the circle x2 + y2 = r2 passes through the origin

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: What is the normal line to the curve 9x4 + 4y = 36 at (0,3) ?

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Q: Prove that all normal to the curve x=acos+atsint,y=asint-atcost.Are at a distance a from the origin

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Q: What is the area of the shaded region of the circle, bounded by the x-axis and the line y=-x,…

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Q: Determine the curve that passes through (5, - 1) such that every normal line to the curve passes…

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Q: If a rectangle has its base on the r-axis and two vertices on the curve y = e-", show that the…

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Q: Construct a smooth curve tangent to the line segments starting at point P. P

A: Given: a group of line segments joining to form a zig-zag figure. Aim to form a curve which is…

Q: Show that the normal line at any point of the circle x2 + y2 = a2 passes through the origin.

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Q: Find an equation of the normal line to the curve  y = sqrt(x)  that is parallel to the line  4x +…

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Q: What is the area of the largest rectangle that can be drawn with one side along the x-axis and the…

A: given curve is y=e-x2 find the largest area of a rectangle which has one side along the x-axis and…

Q: 2. y2-xev-1+ x = 7 at (2,1)

A: Solution:Giveny2-xey-1+x3=7   at (2,1)To find the equation of normalFormula:Equation of…

Q: What are Bézier curves?

A: A curve is an infinitely large set of points. Each point has two neighbors except endpoints.

Q: find the equation of the normal line to the curve y=x^3 + 3/x at (1,4)

A: Solution ) Normal line is perpendicular to the tangent line  So first find slope of the tangent line…

Q: For a χ2-curve with 27 degrees of freedom, find the χ2-value having area 0.01 to its right.

A: It is given that, Level of significance=0.01 Degree of freedom =27 The χ2 critical value can be…

Q: The curvature of any line with slope m in 2-space at any point on it is TTL

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Q: Find the area oF the loop OF the curve. given

A: Integration is the process of finding the anti-derivative function of the given function. The…

Q: find an equation of the normal line to the curve y = x4/4 +16/x4 at (-2,5)

A: Given: y=x44+16x4 for finding equation of normal at given point x1,y1, we slope m of normal at given…

Q: Find the tangent plane and normal line from x2 + y2 + z2 = 30 in (1, -2, 5)

A: Given: -

Q: Prove that all normal to the curve x=acos+atsint,y=asint-atcost. Are at a distance a from the…

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Q: Show that the normal line at any point on the circle x2+ y2 = r2  passes through the origin.

A: Consider the given equation of circle as x2+y2=r2

Q: 1) The equatiqn of the normal to the (urve y= 4x-3x2 at the point (I,1) is :

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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: write an equation of the normal line to the curve y=x^3-3x+1 at the point (2,3)

A: To calculate the equation of the normal line to the curve, first we need to calculate the gradient…

Q: Find the number 6 such that the line y = 6 divides the region bounded by the curves y = x2 and y =…

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Q: At what point of the curve y = x* is the normal line parallel to 2x + y = 3? 2 16 ㅇ (, ) (뚜 든) 이 o…

A: To find  The point of the curve y=x^4 is the normal line parallel to 2x+y=3.

Q: Find an equation of the normal line to the curve y = Vx that is parallel to the line 6x + y = 1. y =

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Q: Find an equation of the normal line to the curve of y = Vx that is parallel to the line 6x + y = 1.…

A: Given that: The curve y = x parallel to the line 6x + y = 1 To find: The equation of normal line to…

Q: What is the slope of the normal line to the curve y= In(xª + 1) at x=1,

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Q: What is the normal line to the curve 9x2 +4y2 = 36 at (0,3)? (А) у-2-0 B X+1=0 Cy-axis D X- axis

A: We need to find the normal equation of the at (0,3).

Q: Prove that there no line through the point (0,1) is tangent to the graph of y = x*.

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Q: The Normal line at the point (0, –1, 1) to the 3 surface exy - xy² + z³ = -2 is 7=y+1=² Select one:…

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Q: The tangent line to a circle may be defined as the line thatintersects the circle in a single point,…

A: The tangent line to a circle may be defined as the line thatintersects the circle in a single point,…

Q: Prove that the normal point on the circle passes through the center.

A: Consider the equation of the circle, x2+y2=r2 Consider an arbitrary point x1,y1 on the circle.…

Q: Describe the condition for a curve to be rectifiable between two points.

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Q: Write the equation of the normal drawn from the point (1, -2) on the circle x²+y²-4x+6y+11 = 0

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

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

A: follow next step

Q: Find the area bounded by the curve ay²=x³ and the line x=4a. With sketch please.

A: Area problem....

Q: The area bounded by the curve y = 6x and the lines x = 7,x = 11 and x – axis ахis is

A: → y = mx is the equation of straight line passing through origin with slope m.→ Area of triangle =…

Q: Find the slope of the normal line y^2=1-x^2 at point (2,1)

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

A: The equation of the curve is y=x and the equation of the line parallel to the normal line is 2x+y=1.…

Q: Determine the equation of the normal line to f(x) = 9/x2 at x = 3

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Q: Find the area between the curve y = sec (4x) and the line joining the points (-,2) and (. 2).

A: Consider the given information: To find the area between the curve and the line joining the points.

Q: Find an equation of the normal line to the curve of y = x that is parallel to the line 6x + y = 1. y…

A: Draw the graph of the given curve and the given parallel line.

Q: Regions under the curve can be described in terms of area. True or False

A: We want to tell you above statement is true or false

Q: Show that the curve for which the normal at every point passes through a fixed point is a circle.

A: We know the equation of a circle is represented by (x-h)2 + (y-k)2 = r2, where (h, k) is centre and…

Q: . Determine the curve that passes through (5, - 1) such that every normal line to the curve passes…

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Q: Find all points on the curv of the tangent line is -1.

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Q: Find the equation of the normal line to the curve 2x/y - 3yvx + 5xy = 22 in the point (4, 1).

A: Given,         The curve is 2xy-3yx+5xy=22 in the point 4,1.