6. Find the equation of the curve whose slope at any point (x,y) is xy and which passes through the (9, 1)

Q: Find an equation of the line tangent to the curve defined by z2 + 6ry +y = 32 at the point (2, 2).

A:

Q: 34. Find the slope of the curve x^2 - 3xy y^2 - 4x + 2y + 1 = 0 at the point (1,-1 O 1/5 1/6 O 1/4 O…

A:

Q: 1 ) Find the equation of the curve for which   y” =  6x – 4 and which passes through (1,2) and (-2…

A:

Q: 2 Find an equation of the line L, where L is perpendicular to y =x and passes through the point…

A: Given a Line L which is perpendicular to  y = (2/3)x  at point (3,2)  Equation of line L is…

Q: Find the equation of the curve that passes through the point (1, 3) and has a slope of at any point…

A:

Q: 2. Find y in terms of x if = 6x² – 2x and the curve passes through the point (1, 5). -

A: We have to find the value of x if dydx=6x2-2x and the curve passes through the point (1,5).…

Q: 5. Find an equation of the line tangent to the curve y = 3x² 1 and parallel to the line 2x – y + 3 =…

A: Explained below

Q: 15. Find the equation of the curve whose slope at any point is equal to -(y +1)/(x + 1) and which…

A:

Q: 5 Find the equations to both lines through the point (2,-2) that are tangent to the parabola y = x²…

A:

Q: Find an equation of the curve that passes through the point (0, -7) and whose slope at the point 2x…

A: we have to find the equation of the curve

Q: Find an equation of the line tangent to the curve defined by x + 3xy+ y = 5 at the point (1, 1).

A: Given  Curve ia x3 + 3xy + y2 =5 at the point(1,1) Find equation of tangent.

Q: 3. Find the slope of the graph tangent to the curve y =x* - 2x3 +x that passes through the point (2,…

A:

Q: 6. Find the member of the curve whose slope at any point is √y and passes through the point (2, 1)

A:

Q: 10. Find the slope-intercept form of the equation of the line tangent to the graph of y arctan(9x)…

A: Given y = arc tan9xand x=39here we find the slope - intercept form of the equation of the line…

Q: Find the curve y = ƒ(x) in the xy-plane that passes through the point (9, 4) and whose slope at each…

A: Given, the curve y = ƒ(x) in the xy-plane that passes through thepoint (9, 4) and whose slope at…

Q: 3) Find all points (x, y) on the graph of x2/3+y²/3 = 8 where the tangent lines have slope –1.

A:

Q: Find the slope of a line tangent to the curve of the given equation at the given point. y = x2 - 3;…

A:

Q: Find the equation of the family of curve whose slope at any point (x,y) is (x+1)/(y-1)

A:

Q: Find the slope of the curve at the given point: y = x(4x − 1)², (1, ²) -

A: Given query is to find the slope of the curve at given point.

Q: 13) Find the equation in slope-intercept form that is tangent to (x- 1)² + (y + 2)² = 25 and passes…

A:

Q: 2. Find the slope of the curve at the point indicated. a. y = 5x – 3x²,x = 1 x-1 b. y =,x = 0 x+1

A: Find the slope

Q: 2) Find the equation of the curve whose slope at any point p(x,y) is m =x (x +5)² and passing…

A:

Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

A:

Q: (4) Find the equation of the line tangent to f(x) = 12√ - 2² at the point (4,8).

A:

Q: 12. What is the equation of the tangent line to the curve y = x² – 2x + 1 at point (3,4)? a. у%3D 2х…

A: Since the student has mentioned to solve question numbers (12) and (13), but we can solve only one…

Q: 1. Find the equation of a curve that passes through the origin and satisfies (1 + x²)y' + 2xy = 4x²

A: Given differential equation is  1+x2dydx+2xy=4x2 Simplify the given differential equation we get…

Q: 25. Find the equation of the line tangent to the curve x2 + y2 = 1 through the point (,).

A:

Q: 6. Find an equation in the form y = ax³ + bx² + cx + d__whose graph has an x-intercept at x = -1, a…

A: Given: x-intercept at  y = 2 y-intercept at x = -1 slope at (-2,-2) is 5. (-2,-2) lies on the curve…

Q: 4. Find the slope of the given function y3 = 4x with points (1, 2) using long method. Plot the curve

A: The solution are next step

Q: Find an equation of the curve that passes through the point (0,1) and whose slope at (x, y) is 11xy

A:

Q: 1. Find the equation of a curve that passes through the origin and satisfies (1+x²)y' + 2xy 4x2

A: To find the equation of the curve

Q: 7. Find the member of the curve whose slope at any point is 2e¹x and passes through the point (0, 1)

A:

Q: 4) Find an equation to the line tangent to y = 5 + |x – 2| at the coordinate (2, 5).

A:

Q: 1 - Find the equation of the tangent line to the curve y = 3 5 x2 +6x 2 11 at its point of…

A:

Q: 9. Find an equation of the line tangent to the curve y = 2x - 7x2 + 10 at the point (3, 1). y = 12

A: Given that, the curve is y = 2x2 - 7x2 + 10  To find the tangent line to curve at point (3,1)   To…

Q: 1. Find the equations of tangent and normal lines to the curve whose equation y2 – 6x2 + 4y + 19 = 0…

A:

Q: -4 The number of tangents to the curve of y=- x³ + 6x? which have a slope of 8 is:

A:

Q: The equation of the tangent to the curve y = x – 3x² – 2x + 2 at the point where the curve cuts the…

A: We have to find  the equation of tangent in the form of y=mx+c.

Q: 5. Find the point on the parabola y=-x+3x+4 where the slope of the tangent line is 5.

A:

Q: 15. Find the equation of the curve whose slope at any point is equal to -(y + 1)/(x +1) and which…

A: We have to find the equation of line when given slope and passing through the point

Q: 4. Find the equation of the tangent lines to the curve y = √x and perpendicular to the line 14x +…

A: We have to find the tangent

Q: 16. Find the equations of the tangent and normal lines to the curve 16x* + y* = 32 at its points of…

A:

Q: Find an equation of the curve that passes through thepoint (0, 1)and whose slope at (x, y) is xy.

A: To Determine: Find an equation of the curve that passes through the point (0, 1)and whose slope at…

Q: 1. find an equation of the line tangent to y = x-3 at point (O,-) %3D

A:

Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

A: To find the equation of family of curves whose slope is given .

Q: 2. Find an equation of a curve satisfying the ff. condition and passing through the point (0, -1).

A: dxy-dy1+x3=0A first order separable ODE has the form of Ny·y'=MxLet y be the dependent variable.…

Q: 15.)) What is the slope of the line tangent to the curve y +2 = - 2sin y at the point (2, 0)? 2 (A)…

A:

Q: ]Find the x-intercept of the curve that passes through the point (0,2) and whose slope at (x,y) is…

A:

Q: 4. Find the slope of the line tangent to the graph of the equation -ey +y° = 7+ 2x at the point…

A: Given query is to find the slope of the tangent at given point.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.