Graph the curves y = x3 - 4x and x =y3 - 4y and find their points of intersection correct to one decimal place.

Q: Use the guidelines of this section to sketch the curve   y =  x - 3x 1/3

A: Let us make a table for the function x -8 -1 0 1 8 y -2 2 0 -2 2

Q: Graph the equation and its tangent. Graph y = x2 - 2x-7 and the tangent to the curve at the point…

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Q: Describe the curve generated by x = 3 + 2t, y = -12 - 6t, for - ∞ < t < ∞.

A: Given: x=3+2t y=-12-6t            - ∞ < t < ∞ To find: curve generated by given functions.

Q: Match the portion of the graph with the corresponding equation that represents the number of…

A: We know that the general equation of the straight liney = mx + bwhere m = slopeb = constant

Q: find the slope of the curve at the point indicated y = 5x - 3x2, x = 1

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Q: Trace the curve x^3 − 6x^2 + 11x − y = 6.

A: Given- x3-6x2+11x-y=6 To draw- The graph of the above function. Concept used- The above expression…

Q: Find the point on the line y = 2x + 8 that is closest to the origin.

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Q: Use a graph to estimate the coordinates of the lowest point on the curve x = t³ - 31, y = 1² +1+1.…

A: Consider the parametric equation x=t3-3ty=t2+t+1 Sketch of the parametric equations is shown below.

Q: Use the guidelines of this section to sketch the curve.   y = x/ x2-9

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

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Q: Find the equation and sketch the graph of the following line. Horizontal with height 3 units above…

A: The equation of a horizontal line is y=c, where c is the y-coordinate of the y-intercept. Hence, the…

Q: Find an equation for the set of points equidistant from the point (0, 0, 2) and the x-axis.

A: To determine the equation for the set of the points.

Q: Find the point on the curve 4x

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Q: Graph the equation and its tangent. Graph y = x2 + 2x - 2 and the tangent to the curve at the point…

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Q: Find the points of intersection of the curves y = 5x2 - 3x - 2 and y = 2x - 1.

A: We have the equation of curves as y=5x2-3x-2            ⋯⋯1y=2x-1                      ⋯⋯2

Q: Use the guidelines of this section to sketch the curve   y = x (x- 4 )3

A: Consider the given function: y=xx-43 Now make a table for function value at different points:

Q: Find the length of the curve Y 12x', 1<X< 2

A: Given curve is: Y=X55+112X3, 1≤X≤2 To find the length of the curve.

Q: Find an equation of the line which is tangent to the circle r +y - dr + by – 12 = 0 at the point (5,…

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Q: Perpendicular to the line 3x - y =-4; containing the point (–2,4)

A: 3x-y=-4 y=3x+4 here coefficient of x is 3 so the slope of the given line is m=3 and the given line…

Q: Determine the nature of the turning points for the curve y = x5 - 5x4 + 5x3 -1.

A: Given function is y = x5- 5x4 + 5x3-1   ......1

Q: Find the y intercept of the line: X+2y-1=0

A: Given line is x + 2y - 1 = 0

Q: Graph the curves y = x√(4 - x2)

A: the given curve is y=x4-x2 we have to graph the given curve. the domain of the given function is:…

Q: Use the guidelines of this section to sketch the curve.   y = 1/ x2 -9

A: Let us plot a table with values of x and y. x y 0 -8 1 -8 -1 -10 2 8.75

Q: 13 4.

A: Slope of the curve at a point  is dy/dx at that point

Q: Find the closest point to the point (2,0) on the y = x curve.

A: To find the closest point to the point (2,0) on curve y=x

Q: Find the point when the line y=-3x+8 that is closest to the origin.

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Q: Find the point on the line y = 2x that is closest to the point (5, 2).

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Q: Find the point on the line y = 2x + 1 that is closest to the point (2, 2).

A: Given: Given equation of the line is y=2x+1 We want to find the point on the line  y=2x+1 that is…

Q: find the slope of the curve x^2+y^2-6x-4y-21=0 at (0,7)

A: Given curve  x2+y2-6x-4y-21=0we find slope at (0,7)

Q: Find the slope of the curve defined by the equation x²y – 8 = 0 at the point (2, 2)?

A: The required slope of the given curve can be found as below

Q: Sketch the curves 1.) y = 3+4x-x2

A: the equation of the curve is: y=3+4x-x2 we have to sketch the given curve.

Q: What point on the graph of y = x² is closest to the point (3,0)?

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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: Let's.

Q: Find the point on the line y = 5x + 4 that is closest to the origin. (х, у) %3

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Q: Find the equation of the line tangent to the graph of y = 4x'-9x-7 at the point (1,8).

A: Method to find tangent at a point of any curve.

Q: Trace the curve: y^2 = 4x^2 / (x+5) (x-2)

A: We want to plot the graph ofy2=4x2(x+5)(x-2)=&gt;y=4x2(x+5)(x-2) The above expression exists…

Q: y = (x-5)(x+1)

A: Given equation of curve y=x3(x-5)(x+1)                   (1) We have to trace the curve of above…

Q: Find the equation of a line that intersects the curve y = x² + 14x + 52 at x = -10 and is parallel…

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Q: Sketch the curves 2.)  y = 36 + 12x - x3

A: This question is taken from the curve sketching in which we have to sketch the given function. We…

Q: Find the equation of the family of curves whose slope at any point (x, y) is 2. y 4. equal to the…

A: We need to find the family of curves. NOTE - As per our guidelines we can not solve multiple…

Q: Find the point of the line y = 2x − 1 that is closest to the origin.

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Q: Find the curve whose slope at any point (x,y) is 6x^2−2x−5 if the curve is required to pass through…

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Q: Use the guidelines of this section to sketch the curve. y = x/7 - x2

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Q: Find the point on the line  y = 5x + 2  that is closest to the origin.

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Q: Determine the nature of the turning points for the curve y = x5 – 5x* + 5x³3 – 1.

A: Turning point of a curve: Turning point is a point where the graph has the highest value (maximum)…

Q: graph y=x2-2x+2 and the tangent to the curve at the point whose coordinate is 1.

A: Topic -graph and tangent to the function

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.