Use implicit differentiation to find the points where the parabola defined by x² – 2xy + y – 6x + 2y + 17 = 0 has horizontal and vertical tangent lines. The parabola has horizontal tangent lines at the point(s) The parabola has vertical tangent lines at the point(s)

Q: Draw a diagram to show that there are two tangent lines to the parabola y = x2 that pass through the…

A: Given: y=x2

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: Find an equation of the tangent line to the curve  2(x2+y2)2 = 25(x2-y2) (a lemniscate) at the the…

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Q: Find the equation of the tangent plane to the graph of f(x, y) = In (14x² – 11y) at the point (1,…

A: Let us considre a two variable function z=f(x,y)  Then the equation of tangent plane  at (a,b) is…

Q: Find the equation of the tangent plane to the graph of (x, y) = In (16x? – 13y²) at the point (1,…

A: We will find the first order partial derivatives fx and fy and then use the formula for tangent…

Q: Draw a diagram to show that there are two tangent lines to the parabola of y = x2 that pass through…

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Q: Use implicit differentiation to find an equation of the tangent line to the ellipse defined by 4x2 +…

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Q: Find the coordinates of all points on the curve x^2 -2y^2 = 5xy-33 where the curve has a horizontal…

A: x2-2y2=5xy-33 →(1)Horizontal tangent slope is 0Differentiate (1) w.r.t…

Q: Find the equation of the tangent plane to the graph of 7y f(x, y) = at the point (4, –1). (Use…

A: We will find the first order partial derivatives and use the formula to find the tangent plane to…

Q: Use implicit differentiation to find the points where the circle defined by 2+3 - 6z 8y =-16 has…

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Q: a) Find an equation of the tangent plane to the surface at the given point. xyz = 15, (1, 3, 5) b)…

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Q: Graph the parabola f(x) = x2 . Explain why the secant lines between the points (-a, f(-a)) and (a,…

A: We have the given equation of parabola as fx=x2 On considering the solution set, which satisfy the…

Q: Find the equation of the tangent plane to the graph of f(x, y) = 3xy² + 2x³y² at the point (-2, 3).…

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Q: Draw a diagram to show that there are two tangent lines to the parabola of y = x2 that pass through…

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Q: Find the equation of the tangent plane to the graph of S(x, y) = In (4x² – y²) at the point (1, 1).…

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Q: Consider the parabola defined by x² – 2xy + y + 4x – 8y + 20 = 0. Use implicit differentiation to…

A: Given: x2-2xy+y2+4x-8y+20=0

Q: 1 Find the x-coordinates of all points on the curve y= 9x* – 48x° – 90x + 9x + 34 where the tangent…

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Q: Find an equation of the tangent line to the parabola y=x2+x such that it passes through the point…

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Q: Find an equation of the tangent line to the parabola y = x2at the point (2, 4).

A: To find the equation of the tangent line to the parabola y = x2at the point (2, 4). For the parabola…

Q: Find the cubic function y = ax3 + bx2 + cx+ d where its graph has horizontal tangent line at (-2,6)…

A: I have written the important facts in the solution part

Q: Find the equation of the tangent line in the given place. complete solution 1.) Tangent to the…

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Q: Draw a diagram to show that there are two tangent lines to the parabola y = x² that pass through the…

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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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 plane to the graph of 5y f(x, y) at the point (4, -7). (Use…

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Q: Determine the equation of the tangent and normal to : 1. The parabola y² = 6x - 3 perpendicular line…

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Q: Find the point (x0,y0) on the graph y=x^3 + 6x^2 +3x -5 at which the slope of the tangent line has…

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Q: Draw a diagram to show that there are two tangent lines to the parabola of  y = x2  that pass…

A: Given the parabola : y=x2Tangent passes through the point 0,-9 We need to find the coordinates of…

Q: Find an equation of the tangent plane to the surface at the given point. x²+²-72²-38, (-3, -6, 1)

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Q: The slope of the tangent line to the parabola y 3x? + 2x + 3 at the point (– 5, 68) is: The equation…

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Q: Example: Find the tangent line to the parabola y = 4x – x² at the point (2,4). Be sure to find the…

A: We have to find the tangent line to the parabola y=4x-x2 at the point 2,4.

Q: Form the diffrential equation representing the family of curves y = a sinx (x + b) where a,b are…

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Q: ) Find equations of the tangent line and normal line to the given curve at the specified point.  y =…

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Q: Find an equation of the tangent plane to the surface at the given point. 5x2 + 2y2 + 5z2 = 73,    P…

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Q: Find the equation of the tangent plane to the graph of f(x, y) = 2xy² + 2x³y? at the point (-1,2).…

A: To find the equation of a tangent plane.

Q: Use implicit differentiation to find an equation of the tangent line to the ellipse at the given…

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Q: Use implicit differentiation to find an equation of thetangent line to the curve at the given point.…

A: We need to find the equation of tangent passing through the point (1,2)

Q: Find the equation of the tangent line to the parabola at the given point. x^2 = 2y, (-2, 2)

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

Q: equation of the tangent line to the curve at the point  ( a , b ) . x2 − xy − y2 = 9     (hyperbola)…

A: Given query is to find the equation of tangent at (a,b).

Q: Find the equation of the tangent plane to the graph of f(x, v) = In (17x² – 14y²) %3D at the point…

A: The given function is f(x,y)=ln17x2-14y2 and the point is 1,1. The equation of the tangent to the…

Q: The slope of the tangent line to a plane curve y=f(x) at the point (x,y) is given by 3 - 2 m=- + 16x…

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Q: Find an equation of the tangent plane to the surface at the given point. x² + y² 7z² = 138, (-8, -9,…

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Q: Find distance between point A(1,3) Perpenclicular the line L: 2y =2+X on

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Q: Find an equation of the tangent plane to the surface at the given point. x² + y2 – 5z2 = 140, (-8,…

A: We will solve the problem

Q: Find a cubic function y = ax3 + bx2 + Cx + d whose graph has horizontal tangents at the points (-2,…

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Q: 13. BONUS: Find the coordinates of all points on the graph of y=1-x at which the tangent line passes…

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Q: Find the cubic function y = ax³ + bx² + cx + d where its graph has horizontal tangent line at (-2,6)…

A: solve the given problem.

Q: 10. At what point on the parabola y = 3x² + 2x is the tangent line parallel to the line 10x – 2? y

A: Given,          The parabola y=3x2+2x is the tangent line parallel to the line y=10x-2.

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: Use implicit differentiation to find an equation of thetangent line to the curve at the given point.…

A: The equation of a tangent to the curve y at point (a,b) can be given as :…