Find equations of both the tangent lines to the ellipse  x2 + 4y2 =36 that pass through the point (12,3)

Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y, (-5, ) 2у, %3D

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Q: At what point does the normal to y = 2 + 2x + 2x² at (1,6) intersect the parabola a second time?

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

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Q: Find an equation of the tangent plane to the surface at the given point. x² + y² – 9z2 = 4, (-2, -3,…

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Q: Find the parabola y= ax2+bx+c that passes through (2,1) and be tangent to the line y=2x + 4 at (1,6)

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Q: 4.) Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

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Q: Find an equation of the tangent line to the astroid at the (3√3, 1).   x2/3 + y2/3 = 4

A: Given an astroid equation find the equation of tangent at a point.

Q: Find the equations of all tangent lines to the curve x² + 4y2 = 8 that pass through the %3D point…

A: The curve x2+4y2=8 that pass through the point (-4, 0). We have to find the equation of all tangent…

Q: Find the equations of the tangent lines to the curve whose parametric equations are x = 2t2 - 4t +…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find the equation of the tangent line to the curve y = IVa at the point (16, 64). %3D y =

A: The standard form of the tangent line helps to find the required equation of the line. The standard…

Q: The slope of the tangent line to the parabola y 2x + 3x +6 at the point (1, 11) is: The equation of…

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Q: Find the parabola with equation y = ax2 + bx whose tangent line at (1, –1) has equation y = 3x – 4.…

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Q: 4. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2, 5/6). Sketch the…

A: To find the trajectories of the hyperbola write dydx by dxdy  and solve the system.

Q: Find the length of the arc of the curve 4y2 = 9x3 from the origin to the point (2,3v2).

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Q: 2. Find the equations of both the tangent lines to the parabola y through the point (3, 16). :-

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Q: Find the parabola with equation y= ax2 +bx whose tangentline at (1, 1) has equation  y= 3x -2.

A: We have to find equation of parabola y=ax2+bx which has tangent y=3x-2 at 1,1 .

Q: Find the tangent plane to the equation 4x2 + 3y2 – y at the point (-4,-1,68) Z =

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Q: Find an equation of the tangent line to the parabola y − x2 - 8x + 9 at the point (3, -6).

A: The derivative of a curve at a point gives the slope of the tangent to the curve. It can be…

Q: Find the parabola with equation  y = ax2 + bx  whose tangent line at  (1, −1)  has equation  y =…

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Q: Find the slope of the tangent line to the "tilted" ellipse at the point (-1, 1). x²+ y² = xy+3 3 3…

A: To find the slope of the tangent line to the ellipse x2+y2=xy+3 at the point -1,1

Q: Find point on the ellipse x^2+2y^2=1  where the tangent line has a slope of 1.

A: We know, slope of tangent line = dydx

Q: Find equations of both the tangent lines to the ellipse x2 +4y2 =36that pass through the point (12,…

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Q: Find the equation of the plane tangent to the graph of z + xyz = 33 at (1,2,3).

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Q: 4. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch the…

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Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0,1) and is tangent to the…

A: Since, the parabola passes through (0,1) ,so,we substitute x=0, y=1 ,to get c=1

Q: Find the slopes of the tangent lines to the ellipse 4x +y = 40 at y=2. The smaller slope is The…

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Q: Find the equations of the tangent lines to the curve whose parametric equations are x = 2t2 – 4t +…

A: We find out dy/dx .then we find out value of t at given points and then find slope of tangent line…

Q: 9) Find the slope of the tangent line to the hyperbola defined by the equation y2 - x2 = 7 at the…

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Q: Find the equation of the tangent to the 2(x² + y²)² = 25(x² – %3D - y²) at (3,1)

A: Given : 2x2+y22 = 25x2-y2

Q: 4. Find the equation of the tangent plane at the point (-2, 1, -3) to the ellipsoid 22 + y? + = 3 4

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Q: Find an equation of the tangent line to the curve 2(a2 – y²)² = 25(x² + y²) at %3D (3, 1)

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Q: Find equations of both lines through the point (-2,-18) that are tangent to the parabola y = x² + 3x

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Q: Find an equation of the tangent plane to the surface z = 2y² – 3x² at the point (-3, -3, -9).

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Q: The slope of the tangent line to the parabola y 4x? + 7x + 3 at the point (0, 3) is: The equation of…

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Q: Find an equation of the tangent line to the hyperbola defined by 5x^(2)+4xy−2y^(2)−4x=19 at the…

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Q: Find equations of both the tangent lines to the ellipse x2 + 4y² = 36 that pass through the point…

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Q: Find the parabola with equation y = ax + bx whose tangent line at (1, 1) has equation y = 5x - 4.

A: ven parabola , y =ax2+bxtangent ,           y = 5x-4comparing with y = mx+c , slope of tangent m = 5

Q: Find equations of both the tangent lines to the ellipse x + 9y2 81 that pass through the point (27,…

A: Given information: The equation of the ellipse is x2+9y2=81. Calculation: We need to find the…

Q: . Find the equations of both lines that pass through the point (2, –3) and are tangent to the…

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Q: Find an equation of the tangent plane to the surface at the given point. 4x2 + 2y2 + 5z2 = 177, P =…

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Q: Find the equations of all tangent lines to the curve x2 + 4y² = 8 that pass through the point…

A: Given curvex2+4y2=8Differentiate above curve w.r.t…

Q: 3// Does the parabola y = 2x2 – 13x + 5 have a tangent whose slope If so, find tangent and normal…

A: Q3    y = 2x2-13x+5 -*      dydx=4x-13if scope of the tangent be -1 thendydx=-1 as than paint of…

Q: Find the equation of the tangent plane to z=6x2+2y2  at the point (1,5)

A: Given  z = 6x2+2y2  at the point (1,5)

Q: Find an equation of the plane tangent and an equation of the line normal to the surface 7z = 4x² -…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Find an equation of the tangent plane to the surface at the given point. + 3x – z2 = 56, (5, -3, 2)

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Q: Find the equations of both of the tangent lines to the ellipse x² + 4y² = 36 that pass through the…

A: Find the slope of curve. Find the derivative of the following function.

Q: Find the tangent lines as directed. To the ellipse x²+2y²=9 perpendicular to the line 4x-y=6

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Q: Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

A: This is a problem of geometry. We will calculate slope of x, y and z at given point and general…