Discuss the sub-tangent and sub-normal of a curve at a point. Find the condition that the curves ax2 + by =1 and a,x +b, y 1 shall cut orthogonally.

Q: ) Find the orthogonal trajectory of the family of curve given by y = In(r³ + b)

A: First formulate a differential equation to eliminate the parameter b . Then replace (dy/dx) by…

Q: Find the tangent and normal line to the curve at the specified condition.  y = x ( 4x - 1 )2 at…

A: The tangent line is a straight line to the curve that touches the curve at a single point. The…

Q: - 6y Find the tangent plane to the equation z at the point (12,24,4) z =

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Q: Find an equation of the tangent plane to the surface xyz = 10, at the given point (1, 2, 5), and…

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Q: Find the length of the subtangent and sub-normal at a point of the curve y= bsin(x/a)

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Q: Find an equation of the tangent plane and a normal line to the surface z = In Vx2 + y2 at the point…

A: Given that: z=lnx2+y2

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: We plug x=√3 and y=2 in the given equation So the point is on the curve

Q: Find an equation of the tangent plane to the surface f(x, y) = x2y at the given point (2, 1, 4) and…

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Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: We plug x=1 and y=0 in the given equation So the point satisfies the equation

Q: 2y + 4 = 0  at the point (1,1).

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Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — 3ху —у? -2…

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Q: Find the equations of the tangent and the normal at the point indicated.   a2y = x3 at (a, a).

A: To find the equation of tangent and normal at the given point.

Q: Find the tangent plane to the equation z = - 32² – y² + 3y at the point ( – 5, 3, – 75)

A: z=-3x2-y2+3y  and the point (-5,3,-75)

Q: Find the equations of the tangent plane and the normal line at point (1,1,-2) to surface z^2 =…

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Q: x = e' and y = te %3D

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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: 1. For the curve x2y2 = 25 at (-1,-5), find the equation of the normal line.

A: The given curve is: x2y2=25 Differentiating it with respect to x: y22x+x22ydydx=0 at (-1,-5):…

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 tangent plane at the given point. f (x, y) = x/√y,  (4, 4)

A: Given : The function is f ( x, y) = xy and point ( 4, 4 ).

Q: Find an equation of the tangent plane to the surface z = 16 − x2 − y2 at the given point (2, 2, 8)…

A: To Determine: Find an equation of the tangent plane to the surface z = 16 − x2 − y2 at the given…

Q: Q4) Show that the point (-1, 0) lies on the curve 6x² + 3xy + 2y2 + 17y – 6 = 0. Then find the…

A: Put x=-1 and y=0 in the equation of curve that is…

Q: Find equations of the following. y = x2 − z2,    (6, 11, 5) find the tangent plane and normal line.

A: According to the given information: Consider the given equation at the given point:

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = (1, 5, 5)

A: Given: The function is fx,y=yx, 1,5,5. The objective is to find an equation of the tangent plane to…

Q: Find an equation of the tangent plane to: 3x +y = z at P(-1,1,-2) %3D

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Q: 13. Find an equation for the tangent plane and the normal line to the surface x? + 2y? - 3z? = 3, at…

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Q: Find the equation of the tangent plane to the graph of the curve f(x, y) = x² + y² at the point…

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Q: Find the equations of the tangent and the normal at the point (2,2) at x² – 2xy + y² +2x + y - 6 = 0

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Q: Find the tangent and normal to the curve a2y=3x at (a,a)

A: Equation of tangent to the curve at x0,y0.                y-y0=m(x-x0) Equation of normal to the…

Q: Find an equation of the tangent plane at the given point. g(x, y) = ely, (4, 1) (Express numbore in

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Q: 2y+ In(xy) +z = 6 at the point (4,0.25, 2)

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Q: Find the orthogonal trajectory to the family of curve given below y²=x²(1-Cx)

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Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(4,0,4) on the…

A: The above problem is solved.

Q: Find the length of the subtangent and sub-normal at a point of the curve X y= bsin a

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Q: Find the equation of the tangent plane and normal line to the surface at the given point. x2 z = 9…

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Q: Find an equation of the tangent line to the following curve at the given point. у %3Dех сos пх, (0,…

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Q: Find an equation of the tangent plane to the surface at the given point. z = 8 – (3, –4, 4)

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Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(8,0,8) on the…

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Q: 19. Find the lines that are (a) tangent and (b) normal to the curve y = x' at the point (1, 1).

A: Given curve: y=x3

Q: Find the equations of the tangent and normal lines to the graph of  (x^2 + y^2)^3 = 8x^2y^2 at…

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Q: Find an equation of the tangent plane at the given point. z = In(x-2y), (3,1,0)

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Q: Find the family of curves in the plane such that in each point P(x,y) of it, the intercept of its…

A: Write the equation of the tangent for the family of curves for any point P (x , y). Assume the slope…

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

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Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. x2…

A: Consider the function fx,y,z=x2+y2-z2-18. ∇fx,y,z=fx, fy, fz=2x, 2y, -2z. At 3, 5, -4, ∇f3, 5,…

Q: Find the equation of the line through the origin auel normal to the line x=y-S,2:2y-3?

A: Let ,     L1 : x-01=y-51    L2 : y-321=z-02L be the required line which passes through 0,0,0 &…

Q: Find an equation for the tangent plane and the normal line to the surface x? + 2y? – 3z² = 3, at the…

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Q: Find an equation of the tangent plane to the surface x2 + y2 + z2 = 9 at the given point (1, 2, 2)…

A: Given equation: x2+y2+z2=9 Consider the given equation, fx,y,z=x2+y2+z2-9=0

Q: Determine the equation of the tangent plane and normal line to the surface at the given point.…

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