Let Q = 4x2 + 6xy+ 4y? . The points on the curve Q = 7 which are closest to the origin are: %3D %3D OA(-눈-)and () (주·주) pue OB. (-V7, V7) and (v7, -V7) Oc. (0, ±1) OD. (tV7,0)

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

A:

Q: 5. Trace the curve r = sinocos³o.

A: Given curve: r=12sinθ cos3θ

Q: Find a parametrization for the curve described below. the line segment with endpoints (4,4) and…

A: Given,  A line segment with endpoints 4, 4  and  6, 1  We have to find the parametrization of the…

Q: * Find the equation of the tangent plane to the surface 9a2²-12xy = 5x2+5 at the ivon Ni Smob point…

A:

Q: Find the exact length of the curve. y = In(sec(x)), Osxs n/4

A:

Q: Find the slope of the tangent line to the curve of intersection of the graph of z = 2x2 + 3xy + 2y2…

A: We need to find slope of the tangent line.

Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — 3ху —у? -2…

A:

Q: Find equations of the Normal plane and Osculating plane of the curve y = 2t, x = 2 sin 3t , z =…

A: Consider the equation of a plane as, ax-x0+by-y0+cz-z0=0 Here, a, b, c, are the slopes in x, y, z,…

Q: 4. y = x2--Inx x = 1 ve x = e

A: Topic- application of derivatives to find angle between curves

Q: In the ry-plane, how many horizontal or vertical tangent lines does the curve ry? = 2+ xy have? None…

A:

Q: Find the tangent plane to the equation z = - 32² – y² + 3y at the point ( – 5, 3, – 75)

A: z=-3x2-y2+3y  and the point (-5,3,-75)

Q: Find the equation of the tangent plane to z = In(x?y) – x/ỹ at (-,4). %3D

A:

Q: find the to the the tang horizontal. X-volves at which the _9x+2 Y = ex curve ent

A:

Q: ) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

A:

Q: Given the curve y² = 5x – 1 at point ( 1,-2 ) , find the equation of tangent and normal to the…

A:

Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — Зху — у?…

A:

Q: set up intergral for the length an of the Curve 3T y%3DZ0* sin cx), 04XE

A:

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

A:

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

A:

Q: Find the tangent plane to the equation z = 2x – 3y + y at the point (1, 2, – 8). -

A:

Q: Find the arclength of the curve y = 3x² + 5 on [0,3].

A:

Q: Find the derivative dydx of the hyperbolic spiral r=aθ.

A:

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 an equation for the tangent plane to z-x-y = 3 at the point (2, 1, 8) Z - ) %3D

A: given z-x2-y2=3 at point 2,1,8

Q: Find the tangent line(s) to the parametric curve given by a = t-9t and y =t at (0, 9) %3D %3D

A: We have to find the tangent line

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

A:

Q: Find the tangent plane to the equation z 5a2 - 4y +5y at the point (5, 5, - 200)

A: The equation of the tangent plane to a surface  is given by fx(x-a)+fy(y-b)+fz(z-c)=0where (a,b,c) =…

Q: Compute the length of the curve given parametrically by x=1/3t^3 and y=1/2t^2 for 0 less or equal to…

A:

Q: Find the equation for the tangent plane to the surface z=-8x2 -4y2  at the point   (2,1,-36)

A:

Q: Find the path of the sloping path y = x² + c such that θ = π / 4 is the angle between the tangents…

A: Slope = 1  Point are (a,b) So equation of tangent      Y-b = 1.(x-a)

Q: Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Since we have to find value of a,b,c and d

Q: Find a parametrization for the line through the point (a, b) having slope m.

A: Given that slope = m , this can be written as <1,m> vector. And point= (a,b)

Q: Find an equation of the tangent plane to: 3x +y = z at P(-1,1,-2) %3D

A:

Q: Find the slope of the parametric curve x = -2t3 + 1, y = 3t2, for - ∞ < t < ∞, at the point…

A:

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

A:

Q: Find the angle between the curve 2y=e-x/2 and y-axis

A: we will see in next step

Q: Find the tangent plane to the equation z 2y cos(5x – 4y) at the point (4,5, 10)

A: Given; z=2ycos(5x-4y) at the point (4,5,10)

Q: Find the tangent plane to the equation z 4e- 4y at the point (8, 16, 4)

A: Let x0,y0,z0=8,16,4 be a point on the given surface. Then, the equation of tangent is…

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

A:

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

A:

Q: A bee was flying upward along the curve that is the intersection of z = x⁴+xy³+12 with the plane…

A:

Q: Find the length of parametrized curve given by  x(t) = 6t2 + 12t, y(t) = -4t3- 12t2 - 9t where t…

A: Consider the parametric curve given by: x(t)=6t2+12t and y(t)=-4t3-12t2-9t for t from 0 to 1. The…

Q: Find a curve in the xy-plane passing through the origin andwhose slope at the point (x, y) is x + y.

A: we have to find a curve in the xy-plane passing through the origin and whose slope at the point (x,…

Q: Find the slope of the tangent to the curve of intersection of the survace 3z =√36 – 9x² – 4y² and…

A:

Q: Find the family of curves in the plane such that in each point P(x,y) of it, the intercept of its…

A: Write the equation of the tangent for the family of curves for any point P (x , y). Assume the slope…

Q: Find the orthogonal trajectories of the family of curves r 5C sin 0, where C being parameter.

A: Follow the below steps to find the orthogonal trajectories. Differentiate the function with respect…

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

A:

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…