Find equations of both the tangent lines to the ellipse x2 + 9y2 = 81 that...

Find equations of both the tangent lines to the ellipse x2 + 9y2 = 81 that pass through the point (27, 3)

Expert Solution

milcah answered 1 year ago

Solve the problem 43) Find equations for the horizontal and vertical tangent lines to the curve...

Solve the problem 43) Find equations for the horizontal and vertical tangent lines to the curve r = 1 - sinθ, 0 ≤ θ < 2π. Please check if your answer is correct with the following: Horizontal: y = 1/4 at (1/2, π/6), y = 1/4 at (1/2, 5π/6), y = -2 at (2, 3π/2) Vertical: x = 0 at (0, π/2), x = -3sqrt(3)/4 at (3/2, 7π/6), x = 3sqrt(3)/4 at (3/2, 11π/6)

Find the equations of the tangent lines to the circle x^2 + y^2 = 9 which...

Find the equations of the tangent lines to the circle x^2 + y^2 = 9 which pass through the point (−7, 2). (Ans.: Using decimal approximations, the lines are approximately y = −0.847493x − 3.932456 and 0.147493x + 3.032456.)

For the curve r=1+sin(theta), find: Location of horizontal tangent lines: Location of vertical tangent lines:

Find parametric equations for the tangent line to the curve with the given parametric equations at...

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

Find equations of the tangent lines to the curve y = (x-1)/(x+1) that are parallel to the line x − 2y = 5.

7) Determine the equations of the lines tangent to the graph of 9?2 + 4?2 +...

7) Determine the equations of the lines tangent to the graph of 9?2 + 4?2 + 18? − 16? − 11 = 0 at the points where x = 0. Where do these two lines intersect?

Find a set of parametric equations for the tangent line to the curve of intersection of...

Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces at the given point. (Enter your answers as a comma-separated list of equations.) z = x2 + y2, z = 16 − y, (4, −1, 17)

Find the equation of the tangent plane and the parametric equations for the normal line to...

Find the equation of the tangent plane and the parametric equations for the normal line to the surface x2 + y2 - z = 0 at the point P(4,-1, 6). Show all steps

Find a set of parametric equations for the tangent line to the curve of intersection of...

Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces at the given point. (Enter your answers as a comma-separated list of equations.) z = sqrt(x2 + y2) , 9x − 3y + 5z = 40, (3, 4, 5)

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.$$ x=e^{-t} \cos t, \quad y=e^{-t} \sin t, \quad z=e^{-t} ; \quad(1,0,1) $$(b): Find the unit tangent vector $\mathbf{T}$, the principal unit normal $\mathbf{N}$, and the curvature $\kappa$ for the space curve,$$ \mathbf{r}(t)=<3 3="" 4="" sin="" cos="" t="">$$

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Find equations of both the tangent lines to the ellipse x2 + 9y2 = 81 that...

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Solve the problem 43) Find equations for the horizontal and vertical tangent lines to the curve...

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