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

Q: Find the equation of tangent plane to this surface at the point where x :1 and y = -1.

A: Given surface is z=f(x,y)=sin(π (3x+2y)) +x2y2 Equation of tangent plane is given by,…

Q: (b) Investigate where the curve y = xy4 - x² is concave up and concave down?

A: Given curve is y=x4-x2 find the concavity of the given curve

Q: Find an equation of the tangent line to the parabola y = x2 -1 at the point (2,3) y 4x-5 Oy - 4x - 9…

A:

Q: Find an equation of the tangent plane to the surface z = x^3- y^2 + 12x + 2y at the point (1, 2, 5).

A: Given: z = x^3- y^2 + 12x + 2y (1, 2, 5)

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 21, (1, 4,…

A:

Q: Find the equation of the tangent plane to the surface at the specified point.

A:

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

A:

Q: The tangent of the parabola x = y² + y + 1 at the point (1,0) is

A:

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: find the equation of the tangent plane of this surface

A: In this question, we check the surface is simple and then we find the equation of tangent plane at…

Q: Show that the line b2xx1 + a2yy1 - a2b2 = 0 is tangent to the ellipse b2x2 + a2y2 - a2b2 = 0 at the…

A:

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

A:

Q: Find the slope of the tangent line to the ellipse 1 at the point 25 slope =

A: Here the equation of ellipse is x29+y225=1 and the point is (m,n)We have to find the equation of…

Q: Find the equation for the tangent plane to the surface at the indicated point. -4x – y+ 2z = 1, P(1,…

A:

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

A:

Q: Find an equation of the tangent plane to the surface at the given point z= 5x - xy3+y2,     (1,1,5)

A:

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

A:

Q: Find the equation of the tangent plane to the surface z = 4 号+ゾ + y² at the point (2, -3, 10)

A:

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

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

A:

Q: ind the equations of the tangent line to the ellipse x² + 4y² + z² = 9, x = 2 at the point (2, -1,…

A:

Q: Find an equation of the tangent line to the parabola y = x - 8x + 9 at the point (1, 2).

A:

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: The x-coordinate of the point where the tangent line to the parabola y=2x^2 at x=1 intersects the…

A:

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 of the tangent plane to the surface at the given point. z = 5 - 2x - y, (3,-1, 1)

A:

Q: Find an equation of the tangent plane to the surface at the given point in the figure below.

A: Consider the given:…

Q: Show by implicit differentiation that the tangent to the ellipse at the point (xo, yo) is yoy a? b2

A: Given equation is Differentiating both sides with respect to x, we get

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

A:

Q: Find the points on the ellipse 2x +y = 1 where f(x,y) = xy has its extreme values.

A: Introduction: When a multivariable function is to be extremized under some constraints, we use the…

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

A:

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

A:

Q: Find an equation of the tangent plane to the given surface at the specified point. z3 бх2 + у2 - 7у,…

A: Solved below...

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

A:

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

A:

Q: Find the equation of the tangent plane to the surface of the equation z = x2 + y2 - 2xy on the point…

A: Equation of tangent plane

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

A:

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 the tangent and normal to the parabola y² - 2x - 4y -1 = 0 at the point (-2,1)

A:

Q: ind an equation for the tangent plane of z = –2x²y – 3x² + y at the point (1, –1, –2).

A:

Q: Give the equation of the tangent plane to each of these surfaces at the point indicated.

A:

Q: Find an equation of the tangent plane to the surface at the given point. 5 —х — у, z = 5 - (3, -2,…

A:

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 an equation of the tangent plane to the given surface at the specified point. = In(x - 3y),…

A:

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

A:

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

A:

Q: Find the equation of the tangent plane to the surface y = 2x² – z² at the point (0,-1, 1)

A:

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

A: