x² Q 6) Find the equation of the tangent to the ellipse y² = 1 at the point (xo, Yo)

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

A: Explained below

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: A particle follows the trajectory x(t) = t3 + 2t, y(t) = 20t – t2 with t measured in seconds and…

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Q: Find an equation of the tangent line to the hyperbola y=3/x at the point (3,1)

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Q: find parametric equations for the given curve. y = x2, translated so that the minimum occurs at…

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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: Evaluate SF dR given that F (x, y) = 2yî + (xy – 2x) %3D and C is the curve in the third quadrant…

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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: 1. Find an equation of the tangent plane to the given surface at the indicated point. 2² + y? – 3z =…

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Q: Evaluate given that F (7, y) = 2yî + (zy – 2r)j and Cis the curve in the third quadrant from the…

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Q: Exercises 3.4/p.170 40 Find the point on The curve ytanx). - < x< here the tangent is parallcl to…

A: Given equation of the curve is y=tanx, -π2&lt;x&lt;π2

Q: Find equations for two lines through the origin that are tangent to the ellipse x - 8x +y +5 = 0. YI…

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Q: Find an equation of the tangent plane to the surface at the given point. 2 x2 + 2z?ey - x = 33, P =…

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Q: Find the tangent to the ellipse x? + y² = 1 at P:(V2,1//2). %3D 4 ソ-Va z-Zol

A: Solution:-

Q: e tangent line to the ellipse 25 = 1 at the point (x, y). 9. %3D s where the slope is not defined?…

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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: Find an equation for the tangent plane to the surface 2° – ay? = 0 at the point (27, 1, 3).

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Q: Eliminate the parameter to find a cartesian equation of the curve x = t4, y = ln(t)

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

Q: Given the parabola y=2x2. A secant is drawn through the 2 points of the parabola, which have the…

A: Basic strategy for this question is that we will find the slope in two ways and then equate them to…

Q: Find equations for two lines through the origin that are tangent to the ellipse x2 – 8x + y² + 3 =…

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Q: Find the tangent plane to the equation z = 6e" -20 at the point (4, 8, 6)

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Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (4, 2, -44).

A: Given: Equation of surface is z=5y2-4x2 and a point -4, 2, -44. To find: Equation of tangent plane…

Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

A: Let's find.

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)

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Q: Find the lines tangent to the ellipse x2/4 + y2/9=1 that contain the point (4, 0).

A: We at first consider the equation of tangent  to x2/4 + y2 /9=1 with slope m. Then we find the value…

Q: Evaluate SF dR given that F (x, y) = 2yî + (xy – 2x)) and C is the curve in the third quadrant from…

A: Given

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: 3. he tangent to the ellipse I at the point P: V2 4. 3. 3w q(w) = 2w+ V2 %3D 3 q(w) = 3w V2w - V2 3…

A: Ellipse tangent

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

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Q: Find parametric equations for the semicircle x2 + y2 = a2, y &gt; 0, using as parameter the slope t…

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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: Find the orthogonal trajectories of the family of parabola described by the equation (y – 3) = = cx…

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Q: Eliminate the parameter to find Cartesian equation of the curve: x=2 sint, y = 5 cost, -n <t<n 6. a

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Q: Find symmetric equations for the tangent line to the curve of intersection of the paraboloid zx +y…

A: Given  The equation of Paraboloid Z=x2+y2 The equation of Ellipsoid 2x2+y2+z2=76

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: Find the equation of the tangent plane to the surface -2² at the point y = 2x2 – (0, –1,2)

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

A: Find the equations of the tangent plane and normal line at the point (-2, 1, -3) to the ellipsoid…

Q: Find parametric equations for the semicircle x2 + y2 = a2, y&gt; 0, using as parameter the slope t =…

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Q: Find equations for two lines through the origin that are tangent to the ellipse x – 4.x + y² + 3 =…

A:

Q: determine the parametric equations of the tangent axis to the ellipse x²/9+y²/4=1 at the point T =…

A: As we know that the parametric equation of ellipse at a point acosθ,bsinθ  is given by…

Q: What is the maximum height of a particle whose path has parametric equations x = t9, y = 4 − t2?

A: The height of the particle is given by it's y position: y = 4 - t2 At the maximum height, dy/dt = 0

Q: Find the tangent line to the ellipse x^2+4y^2=8 parallel to the line x+2y=6.

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Q: Find the tangent plane to the equation z = 5a° + æy? + 2 at the point (2, – 4, - 6)

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

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