Answered: 1. Find the slope and the equation of…

1. Find the slope and the equation of the tangent line to the curve y=x³ at x=-1 2. Find the slope and equation of the tangent line to the hyperbola y=3/x at (3,1)

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

See similar textbooks

Related questions

Q: Find the radius of curvature of a parabola y² - 4x = 0 at the point (4,4). 2

Q: What is the differential equation of the family of ellipses with their centers origin and their…

A: Let us solve the problem using the basic equation of ellipse later we will use different methods to…

Q: 1) Find the parametric equations of the line that is tangent to circle x² + y2 = 25 %3D at point (3,…

A: Given: Equation of circle: x2+y2=25 and tangent at point 3, -4

Q: z=x¯-y¯ at (3,-2, 5)

Q: Find an equation of the tangent line to the curve x2 y? 1 64 9. (a hyperbola) at the point (-4, 7).…

A: Find equation of tangent and the value of m and b

Q: when curve y=arctan(x) is revolved about the y-axis, give the equation of the surface of revolution.

A: To find the equation of the surface of revolution

Q: The graph of the curve described by the parametric equations x = 2t2 and y =t³ – 3t has a point…

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

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

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

Q: Given the equation of an ellips in parametric form x = acost, y = bsint semi axes of the ellipse, t…

A: We have been given the parametric form of an ellipse x = acost, y == bsint where a, b are semi-axes…

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: (7.5.0)- Find an equation of the tangent plane to the surface of z = sin(x – 2y) at the point %3D

A: Given F(x, y, z)=z-sin(x-2y) ∂∂xF(x, y, z)=∂∂x(z-sin(x-2y))=-cos(x-2y)∂∂yF(x, y,…

Q: By differentiating implicitly, find the slope of the hyperboloid x +y? - z = 1 in the r-direction at…

Q: Find the point(s) on the surface xyz = 1 closest to the origin.

A: Given, g(x,y,z): xyz=1 distance from origin is d=x2+y2+z2 f(x,y,z)=x2+y2+z2 square of distance…

Q: On a separate piece of paper, sketch the graph of the parabola y = x² + 9. On the same graph, plot…

A: Sketch the figure.

Q: Find the tangent line. To the ellipse x²+4y²=8 parallel to the line x+2y=6

A: Equation of ellipse is , x2+4y2=8Differentiate w.r.t.x2x+8ydydx=0Subtract 2x from both…

Q: Radiation is focused to an unhealthy area in a patient’s body using a semi-elliptic reflector,…

A: The position of the elliptical reflector is placed such that it contains the one of the focus and…

Q: Find the equations of the lines tangent and normal to the curve given by the parametric equations…

Q: (e) x = 4 – z²

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: 12. Find an equation for the tangent plane to the surface given by 2xy? = 2z2 – ryz at the point (2,…

A: We know that the equation of the tangent plane is: nxx-x0+nyy-y0+nzz-z0=0 Where n→-nxi+nyj+nzk is…

Q: 2 2 the equation of the tangent plane to the surface x² + y² + y² +2²= -1 at the point (2, -3, 4)

A: I am attaching image so that you understand each and every step.

Q: Find the differential equation of the family of ellipses with center at the origin a and the major…

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

Q: Describe the graph of the equation. r = 7 cos ti – 18 sin t j+ k O An ellipse in the planex = 1,…

Q: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

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: The tangents to the rectangular hyperbola xy = c² and the parabola y = 4ax at their point of…

Q: Radiation is focused on an unhealthy area in a patient’s body using a semielliptical reflector,…

Q: Find an equation of the tangent line to the hyperbola defined by 5x^(2)+4xy−2y^(2)−4x=19 at the…

Q: of the points where the parametric equation y = 3 cost 0≤t≤ 2T will have a horizontal tangent.…

Q: Find parametric equations for an object moving clockwise along the ellipse (x2/25)+(y29)=1 beginning…

Q: find a parametric equation for the line that is perpendicularto the graph of the given equation at…

A: Given: x2+y2=25; -3,4 for finding equation of line that is perpendicular to given curve at given…

Q: (a) Where does the normal line to the ellipse x2- x y + y 2 = 3 at the point (1, -1) intersect the…

Q: 22 2 Find the equation of the tangent plane to the level surface xy*z? (– 1, – 1, – 2) = 4 at the…

Q: 11. Show that the tangent to the hyperbola x-y = 1 at the point P(coshu, sinhu) except when vertical…

Q: Find parametric equations for the tangent line to the curve of intersection of the following two…

A: We have to find parametric equations for the tangent line to the curve of intersection of the given…

Q: Find an equation for the tangent plane to the hyperboloid x2+y2−z2=1 at the point (3,1,3).

Q: Find an equation of the tangent plane to the given surface at the specified poin 8x2 + y2 - 7y, (1,…

Q: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

A: NOTE: Refresh your page if you can't see any equations. . The diameter of the dish is 18 feet and…

Q: 31. Find parametric equations for the tangent line to the curve of intersection of the cylinders x2…

Q: Determine the equation of the normal line to the hyperbola x^2 - 4y^2 = 9 at (5,2)

A: We have to find equation of normal

Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x2 +?…

A: Given x2 + z2 = 25 and y2 + z2 = 25 at the point (3,-3,4) Let f(x,y,z) = x2 + z2 - 25 and…

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: A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the…

A: Introduction :

Q: Determine the equation of the normal line to the hyperbola x2 – 4y2 = 9 at (5, 2).

Q: 11. Show that the tangent to the hyperbola x- y = 1 at the pomt P(coshu, sinhu), cuts the x-axis at…

A: We will be using the definition of tangent line to solve the problem

Q: 1) Find the parametric equations of the line that is tangent to circle x² + y² = 25 at point (3, -4)

A: Given, Equation of circle: x2 +y2=25 at a point (3,-4). now, parametric equation of the line is…

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)

Question

1. Find the slope and the equation of the tangent line to the curve y=x³ at x=-1 2. Find the slope and equation of the tangent line to the hyperbola y=3/x at (3,1)

Expert Solution