7. (1 point) Find equations for two lines through the origin that are tangent to the ellipse 212 – 16x + y² +1 = 0 Enter the equation of the line with the smaller slope first. y =. y = Answer(s) submitted: y =

Q: Find equations of both lines through the point (2, –3) that are tangent to the parabola y = x2 + x.…

A: We have to find equations of both lines through the point (2 , -3) that are tangent to the parabola…

Q: Determine the slope of the curve y =1/x+1 at point (−2,−1).

A:

Q: Hello. Can you please explain this problem to me?

A: Slope of the function is the derivative of the function.

Q: What is the equation of the line tangent to the parabola y2=12x at point (2,2)

A: y2=12x  ⇒  4a=12                     a=3

Q: Find equations of both lines through the point (2, −30) that are tangent to the parabola y = x^2 -…

A:

Q: What is the equation of the curve passing through the point (3,-2) and having a slope at any point…

A: We want to find correct option.

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 an equation of a tangeant line to the curve at the given point y=4.9x-x^2, (5,-0.5)

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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: Find an equation of the curve that passes through the point (0, 2) and whose slope is xy?

A:

Q: 8. Find an equation for the line parallel to the line y=-3x and containing the point (-1,2).

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

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Q: Find the equation of the curve that passes through the point (1, 3) and has a slope of y/x2 at any…

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Q: Find the equation of a line tangent to a circle whose equation is x2 + y2 – 4x - 21 = 0 at point…

A: Given equation of circle x2+y2-4x-21=0

Q: Find a parabola with equation y = ax² + bx + c that has slope 4 at x = 1, slope -16 at x = -1, and…

A: We know slope of a curve y=f(x) is given by, dydx=f'(x)

Q: How do I find the equation of the tangent line for this ellipse at the point (5/2,1). (x-1)^2/9  +…

A: Follow the steps.

Q: Find the point on the curve y = /2x + 3 which is closest to the point (5, 0).

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Q: Find a parabola with equation y = ax2 + bx + c that has slope 5 at x = 1, slope −11 at x = −1, and…

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Q: What is the equation of a family of curves orthogonal to 2x2 + y2 = c?

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Q: The slope of the tangent line to the parabola y=4x2+2x+6y=4x2+2x+6 at the point (-3,36) is: ?

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Q: Defermine the equation of the line in standard form passing through the point (-2, 1) and paralel to…

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Q: Find the equation of the curve that passes through the point (3, 2) if its slope is given by y = dy…

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Q: 4)Solve for the family of curves of straight lines with y-intercepts thrice as their corresponding…

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Q: Find the equation of the curve that passes through the point (0, 2) and has a slope of at any point…

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Q: Find the equation of the tangent line to the ellipse 25x2+ y2 = 109 at the point (2, 3

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Q: equation of the curve that passes through the point (0, 6) and whose slope at (x, y) is x/y.

A:

Q: The equation of the curve passing through the point (2, 3) and having slope 6x^2 - 8x + 1 at every…

A: Solution is given below:

Q: B. Find the slope of the curve at the given point. 1. y = 4 – 3x2 at (-1, 1) 2. y = x2 – 5 at (1,…

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Q: Find the coordinates of the point/s on the curve y = 2x2 which are closest to the point ( 9, 0 ).

A:

Q: 2. Find the equation of line pass through the origin and parallel the line with equation y = 2.

A: Point (0,0), equation, y=2

Q: Find the equation of a curve going through the point (3, 7) and having slope 4x² – 3 at (x, y).

A: Given ,Slope of curve is 4x2-3Thereforedydx=4x2-3Taking integationon both…

Q: 2. What is the slope of the line tangent to the curve 8x3 –- y² = 4 at the point (1,-2)?

A:

Q: Find the equation of the curve for which y" = x, and which passes through the point (1, 2) with a…

A: Follow the procedure given below. Here,option is wrong, correct ans i given below with solution.

Q: Find equations of both lines through the point (-2,-18) that are tangent to the parabola y = x² + 3x

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Q: Find the point on the line y = 4x + 3 that is closest to the origin. (x, y) =

A:

Q: Find an equation of the curve that passes through the point (0, 6) and whOse slope at (X, y) is X/y.

A: Given that: Slope of the curve at (x, y)=xy

Q: The equation of the line with slope – 2 that goes through the point ( – 5, – 2) ca the form y = mx +…

A: Given that the slope is -2, the point is -5,-2 and the equation of line is y=mx+b.

Q: Find an equation of the curve that passes through the point (0, 2) and whose slope at (x, y) is x/y.

A:

Q: The slope of the curve y^2-xy-3x=1 at the point (0,-1)

A:

Q: Find the equation of the line tangent to the ellipse x^2 - xy + 2y^2 - 4x + 2y + 2 = 0 if the…

A: given equation of ellipse x2-xy+2y2-4x+2y+2=0 and a line  4y-x+2=0 to find equation of line tangent…

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: Does the parabola y = 2x2 - 7x - 1 have a tangent whose slope is -1? If so, find the point of…

A: Recall: Slope , m= dydx Point - slope intercept form : (y-y1)=m(x-x1) ; where 'm' is the slope

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: 14. Find the slope of the curve y = 2x3 – 3x at (-1 , 1)

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: 3// Does the parabola y = 2x2 – 13x + 5 have a tangent whose slope If so, find tangent and normal…

A: Q3    y = 2x2-13x+5 -*      dydx=4x-13if scope of the tangent be -1 thendydx=-1 as than paint of…

Q: find an equation of the tanfent line to the curve at the given point y = 4x – 3x², (2, –4)

A:

Q: What is the equation of the curve passing through the (1, 16) and having a slope at any point (x,y)…

A: Given- 2xyx2+3 To find- The equation the curve passing though the (1,16) and slope at any point x,y…

Q: 4) Find the slope of the curve y = 3x + 1 at point P (1,2)

A: We need to find slope of curve 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.