Find the orthogonal trajectories of the family of curves y = kx'. = C (C) 3 y³ +x? = C (D) 3 y³ + 3 x³ = C (E)y² + 2x² = C (F) ² + = C (G) 2,² + = C (H) + 3.x³ = C

Q: Find the point(s) on x=3-y² that are closest the point A=(1,0)

A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

Q: The level curves of the function f (x, y) = /2x² + y² – 1 are

A: Explanation of the answer is as follows

Q: Find the orthogonal trajectories of the family of curves y = ax² + 4ax + 4a, where a being…

A: Orthogonal trajectory: If a curve cuts every member of a given family of curves at right angle, then…

Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope -12 at x = -1, and…

A: To find a parabola with equation.

Q: the linearization of (fi,f2) = (x²y+ 3xy², 3x³ + 2xy) at (1,0) to approximate the value at…

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Q: The orthogonal trajectories of the family of curves y = cx² is (A) 2x +y2=k (B) x²+2y² = k © x=ky² D…

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Q: The slope of the curve 2x + Vx + y = y at the point (0, 1) is

A: 2x + √(x+y) = y  So,  √(x+y) = y - 2x So, x+y = (y-2x)² So, x+y = y² + 4x² - 4xy  So, y(1+4x) - y² =…

Q: Which point on the curve y = √x - 4+9 is closest to the point (7, 9)? (x, y) = ( What is this…

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Q: Differentiate the function. r(t) = (3²- + 8)i + r'(t) = (6t)i + ( 132 r'(t) = i + (6t)j r'(t) =…

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Q: f(x) = xª -4 and Perpendicular to the line x - 4y + 1= 0.

A:

Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: (5) Find the curve y = f(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

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Q: The points at which the graph of the equation 8x2+ y² – 16x + 8y + 8=0 has horizontal tangent lines…

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Q: Find the extrema of f(x,y) = -2x² + y taken on the graph of x + y? = 0.

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Q: IT Find the orthogonal trajectories to the given curve -3x y= 3x-1 + Ce C

A: With the help of derivative with respect to x and changes (dy)/(dx) by -(dx)/(dy) Then we find the…

Q: 3.Find the coordinates of the points on the curves y =x3 -3x2-12x+10 with the gradients -2.

A: