A curve on the xy-plane passes through the point (0, a) for some number a, and has the property that the slope of the curve at every point P is three times the y-coordinate of P. Find the equation of the curve.

Q: 7. Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Given a function of the curve, y=ax4+bx3+cx2+dx+e To find the coefficient a,b,c, and d such that the…

Q: 14. What is the slope of the curve at the point (0, x²+y-12r +4y = 5 %3D 0-2

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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).…

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A: H

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Q: Verify that the two families of curves are orthogonal, where C and K are real numbers. Use a…

A: Given  The two families of curves are x2 + y2 = C2 , y = Kx  , where C and K are real numbers.

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A: x2-2y2=5xy-33 →(1)Horizontal tangent slope is 0Differentiate (1) w.r.t…

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A:

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A: Here, there is a little word missing in sentence, 'Find the equation of family of curves whose slope…

Q: Find the curve in the xy-plane that has a slope at each point given by 1 and passes through the…

A: See attached file for a step by step explanation.

Q: The curve y=ax^2+bx+c passes through the point (1,9) and is tangent to the line y=3x at the origin.…

A:

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A: Find the equation for the set of points in an xy-plane that are equidistant from the point P -6,3…

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A: Given that y'=-y5xdydx=-y5x

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A:

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…

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

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Q: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangents…

A: To determine the x-intercept of the curve and slope of the tangent at the intercept.

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Q: Prove that the curves y2 = 4x and y2-6x+1 = 0 touch each other at the point (1,2)

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Q: find the slope of the curve at the given points (x2 + y2)2 = (x - y)2 at (1, 0) and (1, -1)

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

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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

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Q: Prove that the curves y2 = 4x and x2+ y2-6x+1 = 0 touch each other at the point (1,2)

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Q: Find the curve in the xy-plane that passes through the point (4,8) and whose slope at each point is…

A: The curve in the xy-plane that passes through the point (4 , 8 ). Slope at each point is 3√x . We…

Q: Find the equation of the curve, in the XY plane, that passes through the point (2, 2) and is such…

A: Differential equation

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Q: Find an equation of the curve in the xy-plane that passes through the point (2, 3) and has, at every…

A: integration

Q: Find an equation of the curve that passes through the point (1, −2), and has the given slope y′ =…

A:

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…

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A: In this question, slope of curve and point is given and we have to find out equation of cuve.

Q: The tangent line to the graph of y = In(x² – 1) is perpendicular to the line a + y = -1 at the point…

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Q: B. Find the slope of the curve at the point indicated. 1. y = at x = -1 4-x2 %3D 2x+3 2. y = xv1 +…

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Q: Show that the curves 2x2 + 3y2 = 5 and y2 = x3 are orthogonal.

A: To show that the two curves are orthogonal.

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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…

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A: The midpoint of the line joining the points: x1, y1 and x2, y2 is x1+x22, y1+y22. The roots of the…

Q: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangent…

A: To find the x-intercept we plug y=0

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 the point (9, 4) and whose slope at…

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: A curve on the ry-plane passes through the point (0, a) for some number a, and has the property that…

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Q: Find all points (x, y) on the graph of y with tangent lines perpendicular to the line y = 4x - 5. (x…

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Q: Find the condition that the line ax+by=1 may be normal to the curve an-1y

A: Given problem is : Find the condition that the line ax+by=1 may be normal to the curve an-1y=xn…

Q: Find the slope of the curve x3y3 + y2 = x + y at the points (1, 1) and (1, -1).

A: Given,