Show that the curve such that the ratio of the di stance between the normal at any of its points and the origin to the distance between the sam e normal and the point (a, b) is equal to the constant k (k > 0, k = 1)is a circle.

Q: Find the distance between the origin and the normal to the curve y=e2x+x2 at the point where x=0…

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Q: Find the normal to the curve x +y = 2x+2y that is parallel to the line y +x=D0. O A. y= -x+2 O B.…

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Q: 2. Let F = (-y/2, x/2), and let C be the curve shown below. What is F ds? Explain %3D why. y 1 1 2 3

A: The vector field is F=-y2, x2 C1:0, 0→2, 0rt=2t, 0, r't=2, 0 F=0, t Hence, the integral becomes…

Q: ind the tangent and normal to the curve y =2e at the point where the curve meets the y – axis

A: Find the equation of the tangent

Q: Average weight of infants (in pounds) 22.5 20 10 7.5 7.5 2 4 6 8 10 12 14 16 18 20 22 24 Months By…

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Q: Show that the curve y=|x| has no tangent line at the origin.

A: We show that y = |x| is not differentiable at origin.  Therefore there will be no tangent line at…

Q: Find the eguations of normal of the cupve v = 2x - v2at 12.0)

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Q: Find an equation of the normal line to the surface given implicitly by z = sin(xy) at the point…

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Q: Find the equation of the tangent and the equation of the normal to the curve y = x + at the point…

A: We need to find equation of tangent and normal.

Q: 1. Find the slope of the line normal to the curve at (1, 2). y=v5x-x? 4 A. 3 В. -4 С. D. E. None of…

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Q: Find the equation of the line tangent to the graph a the given point using definition and verify by…

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Q: Ex – 4y + 2 = 0 at (1,2) 9, tangent line II to the line 4y tangent line I to the line x – 0 at r = 3…

A: 9. The given curve is x2-xy+2y-2=0, at x=3. Put x=3. 32-3y+2y-2=09-y-2=0y=7. The point on the curve…

Q: 1. Find the set of points in the curve y = A where the tangent lines are horizontal.

A: we have to find the set of points in the curve y=4xx2+1 where the tangent lines are horizontal. as…