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

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

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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: tangent

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

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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: Define tangency for general curves?

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Q: elength of the curve is

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Q: What are Bézier curves?

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

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: Assume every secant line of the curve y = f(x) has slope at least 3. Then every tangent line of the…

A: Given: Every secant line of the curve y=fx has a slope atleast 3.Then every tangent line of the…

Q: Find the equation of the normal line to the indicated curve at the given point. y= 3-5x, (2, -37) I

A: Given,  y=3-5x3, (2,-37) Let y=f(x)

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: Determine the DE of the family of curves and sketch the family of the curves All circles with…

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Q: How can draw a Lorenz curve ?

A: ANSWER: For the given question, we have,

Q: Find the exact length of the curve.

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Q: y=csinx  Identify the curves that intersect the curves under a right angle.

A: Given- y = c sinx To find- Identify the curves that intersect the curves under a right angle.

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 the tangent and normal lines to the curve ペー9ーチ at the Pomt (-62)

A: Given, The equation of the curve  x2-xy+y2 = 7  We have to find the equation of tangent and normal…

Q: What curves have zero curvature?

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Q: Given that the tangent and normal to a curve at point P(x, y) meet the x-axis in A and B…

A: It meets the x axis in A and B respectively and y axis in D and E respectively.To Find: Family of…

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: Illustrates the geometric idea for finding the tangent line to a curve?

A: A tangent to a curve at a particular point is a straight line that touches the curve exactly at one…

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

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Q: Explain Tangent Planes and Normal Lines?

A: According to the question, we have to define the term tangent plane and normal lines. The tangent…

Q: exact length of each of the following curves.

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Q: Find the curvature of the curve =.

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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: Find the slope of the tangent line to the circle r = 4cosθ at the point where θ = π/4.

A: Given- r=4cosθ To Find- The slope of the tangent line to the given circle at the point θ=π4.

Q: Find the equation of the tangent line and normal line to the curve ? = √? − 3 at (4,1).

A: I hope the curve here is y=x-3. Hope it helps you. Thank you.

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: Write the application of Deravative" tangent and normal to a curve" also explain and with example.…

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Q: what is the curve?

A: what is the curve?

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: Show that the curve has no stationary points.

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Q: Find the points on the curve where the tangent is verticle

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Q: Find the DE for the given family of curves. Sketch representative family of curves. - family of…

A: Consider the family of lines whose slope and y-intercept are equal. The equation of a straight line…

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

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Q: Find the curvature of the curve ř= .

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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: Find the differentual equatrion characterizing the family of curves described

A: Given that: ky=x2

Q: Do the curve sketching of the following eqn

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Q: À line that intersects a circle at only one point is called a tangent.

A: Determine whether the given statement is true or false.

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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Q: What is the families of the curve of all circles with fixed radius tangent to the line x=4

A: Given: Families of the curve of all circles with fixed radius and tangent to the line x=4 Let h, k…

Q: Find the exact length of the curve Lou

A: We have to find arc length of curve in required interval .Curve equation is shown below: