ind the intersection of the line r(t) = (1,0,–1) + t(4, 15, 2) and the plane x – z = 6. Give your answer in the form (*,*,*). Express numbers in exact form. Use symbolic notation and fractions where nee intersection point:

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A: as per company guidelines we can solve only first question when multiple question being posted

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A:

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A: We will parameterize C and solve.

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A:

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A: Given

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A:

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A: Consider the points, 4,6      and         7,10 The midpoints of two points is given by the formula,…

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A: Let the 2 points in the line segment be,

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A:

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A:

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A: Our objective is to find the distance betwwn the line and point.

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A:

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A: As per the company policy i can answer only first question for you,more than that leads me towards…

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A: Given point :-  (-5,9,-12) To find:- Distance of given point to plane xy

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A: The solution are next step

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A: Hey, since there are multiple subparts posted, we will answer three subparts. If you want any…

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A:

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A: From the given curve bounded region is shown below:       So,   I=∫x=7x=10∫y=0y=4xdydx

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A: we have to find the point of intersection.

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A:

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A: Common points of the circles simply means the point of intersection of the given circles.

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A: Answer:   (1). b=17   (2). a = -12, 40

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Q: Q5. Prove that the circle {(r, y), x² + y? = 1} is not homeomorphic to the interval [-1, 1].

A: Here we can prove this question using topological property connectedness.

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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.