Show that the normal line at any point of the circle x2 + y2 = a2 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: A circle has its center at (3,-2) is tangent to the line 3x+4y-26=0. Compute the point of tangency…

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Q: What is a line that is tangent to two circles on the same plane.

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Q: Find the normal to the curve y = 1 - x at the point (3, -8).

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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: Show that there is a line that is simultaneously tangent to both the curves y = ex and y = lnx.

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Q: y 2 = 5x at (2, –1)

A: Find the tangent line to the given circle as directed. 2x 2 + 2y 2 =  5x  at (2, –1)

Q: If a circle rolls along a horizontal line without slippage, afixed point P on the circle will trace…

A: We know that if a circle rolls along a horizontal line without slippage, a fixed point P on the…

Q: What are Bézier curves?

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

Q: Find an equation of the normal line to the curve  y = x  that is parallel to the line  4x + y = 1.

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Q: There are exactly two tangent lines from an exterior point to a circle. True or False? O True O…

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

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Q: 2) Find and sketch the circle of cur vature at the point on the curve y = x2 where the tangent line…

A: To find and sketch the circle of curvature at a point on the curve y=x2 , where the tangent line has…

Q: If the slope of the tangent line to a curve at a given point is 0, then the normal line iS A.…

A: The slope of the tangent line to a curve at a given point is 0.

Q: Calculate the length of the tangent line, normal line, sub-tangent and subnormal from: a. 4x² + 9y =…

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Q: consider the curve y=x^2-4x+2 show that the normal to the curve at the point x=1 is 2y-x+3=0

A: TO SHOW THE EQUATION OF NORMAL AT x=1 IS  '2y-x+3 =0' GIVEN y = x2-4x+2 EQUATION OF NORMAL AT x=1 is…

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: Find to) - Isina the enclose by the Curve area and the line <x ハ

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Q: find the length of the latus rectum of the curve rsin^2x=cosx

A: rsin2x=cosxLet us change into cartesian coordinates uvPut u=rcosx and v=rsinxr×v2r2=urv2=uThis is…

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

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Q: If the slope of the tangent line to a curve at a given point is 0, then the normal line is A.…

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Q: :Find the length of nomal and sub-normal at a point on the curve y = 21

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Q: Prove that all normals to the curve x= acosx+atsint,y=asint-atcost are at a distance a from the…

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Q: Where does the normal line to the parabola y= x- x2 at  the point (1, 0) intersect the parabola a…

A: Normal to a curve is a line which is perpendicular to the curve at its point of intersection with…

Q: Find the 0lar eauatiDo for the curve represented by the given Cartesian euation.

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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: Chebyshev's theorem is used when there is a bell shaped curve

A: Chebyshev's theorem is used when we want to find the the upper bound  of the probability. And they…

Q: Find the points on the graph of circle defined as (x – 1)2 + (y + 3)2 = 16 where the normal line is…

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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: what is the normal equation to the curve which is the circle with center at origin and and radius of…

A: Given circle , With center at origin (0,0) And a point on circle is (4,3)

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 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: 2. Use the guidelines to sketch the curve. Y In x x²

A: The given function is: y=ln xx2 Note that the domain of the function is (0,∞). First of all, let's…

Q: Which of the following centers of circles that can be tangent to the line x + y = 4 at point (1,3)…

A: Given that equation of tangent to circle is x + y = 4 at point (1,3).

Q: Find the slope of the normal line to curve x=4sint, π y=cos2t when t=-

A: Given that x=4 sin ty=cos 2t Find the slope of the normal at t=π4 find the slope of normal and then…

Q: Find the distance between line 2xy + z = 4.

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

A: Assume that we have the circle of equation x2+y2=r2 and we want to get the normal equation at x0,y0.…

Q: n to find the equation of normal line to the circle y? + x2 = 1 at the point

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Q: Find the area of the circle whose center is at (2, -5) and tangent to the line 4x+3y-8=D0

A: Area of the circle = 9π sq.units

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: Find the length of the tangent line segment from (9. 13) to the circle x2 + y2 = 25.

A: The tangent to circle is the line that touches the circle at a point. The line from center of the…

Q: Determine the length of the latus rectum of the curve y² = 8x

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Q: The curvature of any line with slope m in 2-space at any point on it is 0

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Q: etermine if XY is tangent to circle Z

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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: 2. Circles with fixed radius r and tangent to the y-axis.

A: Solution is given below:

Q: Find the normal form of the line 3x + 4y – 10 = 0 and its where distance from the origin.

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Q: What is the equation of the normal to the curve which is a circle with center at origin and radius…

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