Draw a diagram to show that there are two tangent lines to the parabola of y = x2 that pass through the point (0, -25). Find the coordinates of the points where these tangent lines intersect the parabola. (C smaller x-value (x, y) = larger x-value (x, y) =

Q: The slope of the tangent line to the parabola 2x + 4x + 5 at the point (3, 35) is: The equation of…

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

A: We have to find equations of both lines through the point (2 , -3) that are tangent to the parabola…

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: 5. Find the equations of the tangent line and normal line to the parabola y = 2x² at the point…

A: Since, you have asked multiple questions , according to our guidelines we are supposed to answer…

Q: Find an equation of the plane tangent to the graph of g(r, y) = 3ev²-z² at the point where (x, y) =…

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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 the equation of the tangent plane to the surface 4 =1 at the point 9. 16 (1,-3,2)

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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: Draw a diagram to show that there are two tangent lines to the parabola y = x 2   that pass through…

A: Explanation: Given that,                     Assume that, point of tangency is (a, a2). Slope of…

Q: Find an equation of the tangent plane to the given surface at the specified point. 2. (-16, 4, -1)

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Q: Find an equation of the tangent plane to the surface z = -2z² – 2y?- lz 2y+ 3 at the point (5, 1,…

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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: Find the point (xo, yo) on the graph of y = x' + 9x² + 6x – 3, at which the slope of the tangent…

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Q: 8. At what point of the parabola is the tangent line parallel to 7x+y-2=0? y = 2r-3x +1 O (1,0) O…

A: Here is the solution:

Q: 4. Determine the slope of the common tangent to the parabolas y=x² +1 and y=-x² - 1. y=x*2+1 (a, 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: The slope of the tangent line to the parabola y = 2x + 2x + 6 at the point (- 1, 6) is: The equation…

A: The slope of the tangent line to the parabola                      y = 2x2 + 2x + 6 at the point…

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 for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

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: The slope of the tangent line to the parabola y = 4x? + 7x + 2 at the point (– 4, 38) is: The…

A: Equation of parabola,  y = 4x2 + 7x + 2 Given point is (-4, 38)

Q: 8. Determine the equation of the plane tangent to z point (x, у, z) 3 (-2, 1, 4). x*y3 at the =

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Q: Determine an equation for the tangent plane to the graph of z = 2 + 2 vy + - 7 at the point (1, 2,…

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

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Q: Find the point (xo, yo) on the graph of y = x + 3x² + 4x – 5, at which the slope of the tangent line…

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Q: Find the equations of the tangent line and normal line to the parabola y=2x2 at the point (2,8).

A: We find dy/dx at x=2 to find the slope of the tangent  Then we use the point-slope formula to find…

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y? - 32? . = 82, (-7,…

A: Given equation  x2+y2−3z2=82,     (-7,-6,1)

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

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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: 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: Find an equation of the tangent plane to the surface at the given point. fx, у) %3 х2 - 2ху + у2,…

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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 point (xo, yo) on the graph of y = x + 9x2 + 3x - 4, at which the slope of the tangent line…

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Q: Find an equation of the tangent plane to the surface at the given point. z = 8 – (3, –4, 4)

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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 the tangent plane to the equation z = x2 + 5y² + 3y at the point (-5,-2,39)

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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 equation of the tangent plane to the surface 4 = 1 16 at the point 9. (1,-3,2)

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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: 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: 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: 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)

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…

Q: ) Find an equation of the tangent plane to the paraboloid defined by -- 4x² + 5y² at the point (,-2,…

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Q: Find an equation of the tangent plane to the surface at the given point. xy2 + 3x – z2 = 56, (5, -3,…

A: Given:   xy2 + 3x - z2 = 56  Point ( 5 , -3, 2 )

Q: Find an equation of the tangent plane to the surface at the given point. - . z = 8 —х — у, 3 (3, –4,…

A: Given plane is z=8−83x−y. We have to find the equation of tangent plane to the surface at the point…