A curve passes though (1,4) and (2,1). If y"=2, what is the equation of the curve?

Q: Give the equations of the lines through the point (0, 9) that are tangent to the curve y x + 4 Use…

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Q: The curve y = ax2 + bx + c passes through the point (2, 32) and is tangent to the line  at the…

A: Given curve: y = ax2 + bx + c passes through (2,32) and  (0,0) line at the origin is tangent to the…

Q: The slope of the tangent line at any point (x, y) on a curve is 2/x. If the point (9, 3) is on the…

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Q: Find equations of the tangent line and normal line to the curve  y= x sqrt x  at the point  (1,1) .…

A: Given curve: Let the slope of the tangent line to the given curve is m. And the slope of the normal…

Q: The slope of the tangent line to the curve y=2x^3 at the point (-4,-128) is ____. The equation of…

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Q: Find an equation of the curve that passes through the point (1, 3), and has the given slope y′ =…

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Q: Find the equation of a curve whose tangent line has slope 2x – 5 and the curve passes through the…

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Q: Find equations of the tangent line and normal line to the curve y = x/x at the point (1, 1).…

A: y=xx

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 the equation of the line tangent to the curve (x-2)^2=-4(y+3) at (2,-3)

A: Given data:     The expression for the equation of the curve is: (x-2)2=-4(y+3). The given point is:…

Q: Find the equation of the curve that passes through the point (6, 6) if its slope is given by dy = 7x…

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Q: he slope of the curve 2y2=ax2+b at (1,-1) is -1.Find a,b

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Q: Find the equation of the curve that passes through the point (8, 8) if its slope given by dy 3D 7х —…

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Q: A curve passes through the point (0,5) and has the property that the slope of the curve at every…

A: Slope of the curve is given by dy/dxdy/dx is twice the y coordinate. So, dy/dx=2y

Q: The path of a fast moving particle assuming constant speed traces a circle with equation (x-3)2 +…

A: Given - The path of a fast moving particle assuming constant speed traces a circle with equation…

Q: ) Find the equation of the line normal to the curve x'y+ y'x = 10 at point (1,2).

A: Slope of a normal to the function y=f(x) at point m,n is given by the value of -dxdy at m,n Equation…

Q: 3 at the point 6, 2 The slope of the tangent line to the curve y |3| is: The equation of this…

A: Derivative y with respect to x and then substitute the given point to find the slope.

Q: A curve passes through the point (0, 5) and has the property that the slope of the curve at every…

A: A curve passes through the point (0, 5) and has the property that the slope of the curve at every…

Q: 17. Passes through the point (2, 1) and is perpendicular to y = -x+ 3.

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Q: The slope of the tangent line at any point (x, y) on a curve is 2/r. If the point (9, 3) is on the…

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Q: There are two lines passing through the point (5,-1) that are tangent to the parabola y = -x^2+4x.…

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Q: The slope of the tangent line to the curve  y=3x^3 at the point (-5,-375) is:? The equation of this…

A: Consider the given: y=3x3Differentiate w.r.t. "x"dydx=9x2Find the slope at…

Q: The slope of the tangent line to the curve y at the point ( 5, is: The equation of this tangent line…

A: Given curve is : y=3x To find the slope of tangent at the point 5,35 and equation of tangent in the…

Q: 8. Find the point on the curve y = √2x 3 from the point (1, 4)-

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Q: Find an equation of the curve that passes through the point (0, 2), and has the given slope y′ =…

A: y'=x4y, (0,2) Formula ∫xndx=xn+1n+1+C

Q: Give an equation for the tangent line to = 1 at the y2+1 point (5,2) and sketch it on the graph. -5-…

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Q: Find the equation of the curve that passes through the point (7,3) if its slope is given by dy = 7x…

A: As per our company's policy, we can solve first question only. Please repost other question…

Q: Find the equation of the tangent line to the curve at the given point. Illustrate by graphing the…

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Q: The point (3, 2) is on a curve and at any point, (x, y) on the curve, the tangent line has a slope…

A: Given Slope of tangent line at (x, y) is 2x-3 and Curve passes through (3,2)

Q: The slope of the curve 2y = ax + b at (1,-1)is -1.Find a, b.

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Q: The slope of the tangent line to the curve y 3 at the point 9, is: 3 The equation of this tangent…

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Q: Find the equation of the curve that passes through the point (5,4) if its slope is given by…

A: dydx=5x-2dy=5x-2dxIntegrate on both sides

Q: Find the equation of the curve if = 2(3x – 2) and which passes through ( 1 , 2 ) and ( - 2,5). dx2

A: The given equation is a differential equation, hence integration helps to find the solution to the…

Q: Find the equations of the tangent lines to the graph of y=x²+6 that go through the point (0,-2) and…

A: Given problem:- Find the equations of the tangent lines to the graph of y = x2 +6 through the point…

Q: Find an equation of the curve that passes through the point (0, 4) and whose slope at (x, y) is x/y.

A: Solution:find the equation of curuepasses through the point (0,4)slope of cwue is xydydx=xyy dy=x…

Q: A curve contains (3, 7) has slope of tangent line is 4x – 5. What is the curve equation?

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Q: The slope of the tangent line at any point (x, y) on a curve is 2vx. If the point (9.3) is on the…

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Q: The curve with equation y2 = 5x4 - x2  is called akampyle of Eudoxus. Find an equation of the…

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Q: Find an equation of the curve that passes through the point (8, 2), and has the given slope y′ =…

A: Solution:-We have to find an equation of the curve that passes through  the point (8,2) and having…

Q: slope of the tangent to the curve y2x+ y2x2 =6at (2,1) is

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Q: Find an equation for the line tangent (in general form) to the circle at point (4,-3). The circle…

A: For the figure  given below: Equation of a tangent to a circle at point (a,b)  with radius r and…

Q: 1. The point (5,2) lies on the curve y =Vx-1. Find the slope (correct to six places) of the secant…

A: Since you have posted a question with multiple sub-parts, we will solve first three Sub-parts for…

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: Suppose the slope of the tangent line at any point is vx – 1 . What is the equation of the curve if…

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Q: Find an equation of the tangent line to the curve at the given point. y = 7x2 - x3, (1, 6) y =…

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Q: Find the equation of the curve that passes through the point (6,6) if its slope is given by dy/dx =…

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Q: A line passes through points (5, 8) and (10, a), where a is a parameter. The equation of this line…

A: A line passes through points (5, 8) and (10, a), where a is a parameter. The equation of this line…

Q: At point (1,y), what is y?

A: Note:- If two points is given in Cartesian form like  (2,5)  Then  x=2 and y=5 Means first one is…

Q: The equation of the tangent line to the curve X2+y2=169 at the point (5,-12) is

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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.