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

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: Find an equation of the normal line to the parabola y= x2 -5x +4that is parallel to the line  x-3y…

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Q: ind the point P on the line y = 5x that is closest to the point (78,0). What is the least distance…

A: This question is related to straight line. we will solve it using the condition of shortest distance…

Q: Prove that for any point (a, b) ≠ (0, 0) on the parabola y = x2 , the normal line intersects the…

A: The given equation of parabola is y=x2  For the point (a,b)≠ (0, 0), the slope of normal is and at…

Q: Find the tangent/s as directed to the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x –…

A: The objective is to find the equation of tangent line to the parabola x+2y2+2x-y-3=0 which is…

Q: Sketch in the two level curves of: f (x, y) = y+ x² = k _for k = 1, 2.

A: Solution is written in below steps.

Q: Find the tangent/s as directed:to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x –…

A: Given equation of line is  x-4y=24y=x-2 y=14x-12 So comparing with the slope equation formula,…

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 the points on the curve 9y = x where normal to the curve makes equal intercepts with the axes.

A: Since, the equation of curve is given by 9y2=x3-(i)⇒y2=x39⇒y=±x33Differentitaing equation-(i) both…

Q: Find the x Coordinate of the point on the graph of 4=x² where the to the Secant. Longent tine.…

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Q: find the are bounded by the given curves y^2=2ax,y^2=4ax-a^2

A: The two equations represent parabolas. First both parabolas will have origin as vertices. The region…

Q: Find the exact length of the curve. y = In(sec(x)), Osxs n/4

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Q: Find the points on the surface ( y + z)^2 + (z - x)^2 = 16 where the normal line is parallel to the…

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Q: Find an equation of the normal line to the parabola y = x – 9x + 5 that is parallel to the line x -…

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Q: Find the area of the inner loop of the curve r= 1-2cos θ

A: For the inner loop of the curve 1-2cos θ=0⇒2cos θ=1⇒cos θ=12⇒θ=cos-112⇒θ=π3,5π3

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 the exact length of the curve. y = In(1-x), 0sxs 8.

A: Given that: y=ln 1-x2, 0≤x≤18

Q: Find an equation of the normal line to the parabola  y = x2 − 4x + 1  that is parallel to the line…

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Q: 5. Consider the two curves y = x° - 3x + 20x + 88x² + 71x – 74 and y = 2a+ 50x – 22x + 42.x + 31. |…

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Q: Find the equations of the normal line to the surface z = at the point (1, - 2, 32). - t + 32 ||

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Q: Find an equation of the normal line to the parabola y = x2 - 5x + 4 that is parallel to the line x -…

A: y=x2-5x+4 Differentiating with respect to x, we get dydx=2x-5 Now slope of the normal line is,…

Q: The length of the curve y = from x = 0 to x 6 is

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Q: Find an equation of the normal line to the parabola y = x2 – 8x + 4 that is parallel to the line x –…

A: Let the equation of the normal line in the slope-intercept form is, y=mx+c where m is the slower and…

Q: Find an equation of the normal line to the parabola y = x 2 - 5 x + 4 that is parallel to the line…

A: Given:       y=x2-5x+4 is parallel to the line x-3y=5.

Q: Find the exact length of the curve y = In(1 – x²), 0 Sx S

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Q: Find the minimum distance from the point (6, 0, 9) to the plane x - y + z = 5. (Hint: To simplify…

A: Given plane is x-y+z=5 and the point is (6,0,9) normal to the plane is (1,-1,1)

Q: Find the length of the curve given by S(x) = (a -) defined on the interval (1, 2].

A: Consider the given curve:

Q: Find the minimum distance from the point (6, 1, 6) to the plane x - y + z = 6. (Hint: To simplify…

A: To find the minimum distance from the point (6,1,6) to plane x - y + z = 6. By using formula,…

Q: Find the equations of the normal line to the surface z = 2x°y* at the point (2, 2, 256). y = 2 = -t…

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Q: The area bounded by the curve y= 4x and the lines r = 7,1 = 10 and x - aris is O 4900 square units O…

A: From the given curve bounded region is shown below:       So,   I=∫x=7x=10∫y=0y=4xdydx

Q: Find the length of the curve y=z from z 0 to z=4.

A: The length of the curve is given by:

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: Verify Green's Theorem for: f4y³dx-2x²dy where C, oriented anti-clockwise, is composed of the…

A: To find the integral ∮C4y3dx-2x2dy where C is the positively oriented closed curve x2+y2=9, y≥0 and…

Q: Find the minimum distance from the point (6, 0, 5) to the plane x - y + z = 3. (Hint: To simplify…

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Q: - x = 1 - y', x= y² – 1

A: topic - area bounded by curves

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 length of the tangent to the circle x²+y²-2x-3y-1=0 from the point (2,5).

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Q: Find the length of the tangent to the circle x² + y² − 2x − 3y − 1 = 0 from the point (2, 5)

A: Solution- The equation of the circle x2+y2-2x-3y-1=0 The point =2,5 length of the tangent

Q: Evaluate f. y3 dx - x3 dy where c is the circle x2 + y2 = 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: Find an equation of the normal line to the parabola y = x2 - 8x + 9 that is parallel to the line x -…

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Q: Find the equation of the normal lines to the curve y=x^3-2x+1 that is perpendicular to the line…

A: Consider the given equation of the curve as y=x3-2x+1. Differentiate with respect to x we get as…

Q: Consider the region in the fourth quadrant between the circles x² + y² = 4 and x² + y² = 25 and…

A: answer is in next step. please give a like !!

Q: For the curve x - 2t and y = t-1, what is the equation of the normal line when t=2

A: Given,x=2t.................(1)andy=t-1..................(2)Now,Differentiating both the equations…

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

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Q: Find the equation of the tangent plane and the normal line to the surface z=-2x -8y at the point…

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Q: Find the exact length of the curve. y = In(1 - x²), o sxs

A: Find dy/dx, then put it in the arc length formula.