1. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch es. %3D

Q: Show that the equation of the tangent line to the hyperbola                        x2/a2 − y2/b2 = 1…

A: Given Data The equation of the hyperbola is x²/ a²- y²/ b²=1. The points are (x0,y0).…

Q: Find the orthogonal trajectories for the family of curves, sin? y C In x.

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Q: Show that the tangent lines at the points where the ellipse x² – xy + y² = 3 cross the x-axis are…

A: Explained below

Q: Determine the orthogonal trajectories of the hyperbola 3xy= 5 at the point (2, 5/6). Sketch the…

A:

Q: Find a parametrization of the right branch (x > 0) of the hyperbola(x/a)2−*(y/b)2= 1 using cosh…

A: Given that. xa2-yb2=1     ...(1) Need to evaluate parametrize form of (1).

Q: Find equations of both the tangent lines to the ellipse x2 + 4y 36 that pass through the point (12,…

A: see below the calculation and answer

Q: 7. Derive the orthogonal trajectories of the family of hyperbolas xy = c. %3D

A: The solution are next step

Q: Find the equations of the tangent line in the given plane. Tangent to the parabola z = x² + 3y² , x…

A: Tangent line equation problem....

Q: Find all points on the ellipse x2 - xy + y2 = 1 at which the tangent line is horizontal.

A: The given equation of ellipse is,

Q: Find the family of oblique trajectories that intersect the family of the paraboles y = Cx at angle e…

A:

Q: Find the orthogonal trajectories of the family of curves r² + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: Find the equation of the tangent line to right branch of the hyperbola π π ㅠ x = sect, y = tant, st≤…

A:

Q: Find . F dR such that F(x, y) = (2y, xy – 2x) And I is the curve in the 3rd quadrant from the point…

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Q: Find the orthogonal trajectories of the family of hyperbolas xy = c

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Q: Find the orthogonal trajectories of the family of parabolas with vertices at the origin and foci on…

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Q: whose x-coordinates are equally ine with parabolic runout conner

A: Given as.     python code :

Q: Find the equation of the tangent to the hyperbola x² – 3y² = 1 at the point S(2,-1). A) 2x + 3y – 1…

A:

Q: Find the tangent lines as directed. To the ellipse x²+4y²=8 parallel to the line x+2y=6.

A: Given query is to find the equation of the tangent.

Q: Which of the following is the orthogonal trajectories of the family of ellipses 2x² + y² = a? xy = C…

A:

Q: Find an equation of the tangent plane to the surface at the given point in the figure below.

A: Consider the given:…

Q: Find the equation of the tangent line to right branch of the hyperbola π π x = sect, y = tant, ≤t≤at…

A: Given :x=secty=tant

Q: Find the equation of the tangent and normal to the parabola y=4ax at the point (at²,2at)

A:

Q: 4. Find the equation of the tangent plane to the surface ew + In(xz) - evz = 0 at the point (1,0,…

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Q: determine the equation of the orthogonal trajectories of the following fsmilies curves: Circles…

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Q: Show that the equation of the tangent line to the hyperbola x2/a2 − y2/b2 = 1 at (x0, y0) is x0x/a2…

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Q: 4. Find the equation of the tangent plane to the surface ey + In(xz) – evz = 0 at the point (1,0,…

A: Given:

Q: 4. Consider the equation of the hyperbola given by x2 + 2xy – y² = 7. Find an equation of the…

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Q: Find the orthogonal trajectories of the family of curves x² + Y? = R? %3D

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Q: Determine the equation of the normal line to the hyperbola x - 4y- = 9 at (5, 2). 8x + 5y – 50 = 0…

A: Given equation of hyperbola is  x2-4y2=9          ...(1) We have to find the equation of the normal…

Q: Find the equation of the tangent line to the curve y = et at the point (0, 1). Give your answer in…

A: Given,            The curve is y=exx2+1 and the point is 0,1.To find : Find the equation of the…

Q: Exer. 35-36: Find equations of the tangent line and normal line to the hyperbola at the point P. 3…

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Q: 1. Find the equation of the tangent lines to the ellipse x² + 4y = 8 perpendicular to the line x +…

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Q: Exer. 35-36: Find equations of the tangent line and normal line to the hyperbola at the point P. 35…

A: As per guideline we have to solve one question

Q: The tangent and the normal to the parabola y²=20x at the point T(5,10) meet the x-axis at the points…

A: Details solution is given below:

Q: Determine the orthogonal trajectories of the family of circles (equation below) that is tangent to…

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Q: Find the family of orthogonal trajectories of the family of hyperbolas x²-4y² =k

A: We need to find the family of orthogonal trajectories of the family of hyperbolas x²-4y² =k

Q: Determine the equation of the normal line to the hyperbola x^2 - 4y^2 = 9 at (5,2)

A: We have to find equation of normal

Q: Which of the following points do not lie on any tangent line of the parabola y = x2 + 2? (2,6) O…

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Q: Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle 0…

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Q: Find the equation of tangent line to the parabola y² = 6x – 3 which is perpendicular to the line x +…

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Q: Find the diffrential equation of for each of the curves determined by the condition that at each…

A: length of subtangent =ydydx

Q: Determine the equation of the normal line to the hyperbola x2 – 4y2 = 9 at (5, 2).

A:

Q: Find the orthogonal trajectories of the family of curves r 5C sin 0, where C being parameter.

A: Follow the below steps to find the orthogonal trajectories. Differentiate the function with respect…

Q: Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle e…

A: The answer is given below:

Q: Compute y ds over the part of the parabola y =2Px, for P > 0 starting at (0,0) at (2P,2P).

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Q: ind the equation of the tangent line to right branch of the hyperbola == sec t, y= tant, 2 - sts at…

A: Topic:- application of derivatives

Q: Find the equations of the tangent line in the given plane. Tangent to the parabola z = x² + 3y² , x…

A: Given :                    z = x2 + 3y2      at the point (1,2,13)