Find the point on the line L1 : x = 3 – t, y = 1 + t, z=t, and the point A= (0, 1, 6) The point closest on L that is closest to the point A is I Select ] and the square of the distance between this point and point A is ( Select ]

Q: Qz Find of the lines the point of inter section Linei X = 2 ti +1g y=3t,+29Z=4tı73 Line 2 x = t2 +2,…

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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: 5) s how that the line af intersection f the Planes X+24-22= 5 and 5x-2y-73D0 is Parallel to theline…

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Q: Ex: Find the distance between the pt G(4₁-4,4) and the line x=2t₁ y=Z-3, z = at +2₂

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Q: (x- 2y) dA on the parallelogram P bounded by y = 5 – 2x, y = 7- 2x, y = 3x – 6, and y = 3x + 2. Use…

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Q: 2. Consider any five points P1, Ps in the interior of a square S of side length 1. Show that one can…

A: To solve this problem we use the Pigeonhole principle . Pigeonhole principle : If there are m holes…

Q: Find the distance from point P(1,1,1) to the pl r +y +z = 1

A: We have to solve

Q: An angle with its vertex at the origin of an xy-coordinate plane and with initial side on the…

A: We know, An angle with its vertex at the origin of an x-y-coordinate plane and with initial side on…

Q: 2. Consider any five points P1, Ps in the interior of a square S of side length ... 1. Show that one…

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

Q: Find the points on the graph of z = xy + 8y where the tangent plane is parallel to 9x + 5y + 9z = 0.…

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Q: distance

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Q: The set of points P(x, y) such that their distance from (3, 0) is v2 times their 1. distance from…

A: The   distance from point Px,y  to 3,0 is 2 times the distance from point Px,y  to 0,2. Solution:…

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

A: Given: Curve x=3-y2 and a point A(1,0).

Q: Find distance the poinl- the between Cziz16) f * +y=0, J - Z =1 the line

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Q: Parallel unes /perpendialar Through point Wnat is an equation of the line that, passes through the…

A: If two line are parallel their slopes are equal

Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y = -2t z = 2t 3

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Q: 9. Find the point (x, y) on the line y = 2x + 3 such that the distance from (x, y) to (1, 1) is as…

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Q: Find the points on the graph of z = xy +8y where the tangent plane is parallel to 9x + 5y + 9z = 0.…

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Q: Where should the point P be chosen on line segment AB so as to maximize the angle 0? (Assume a = 4…

A: Given that  The figure is

Q: The distance from a point (2, y) to a line x – 2y + 3 = 0 equal to v5. Find the value of

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Q: and the line perpendicular to Find the area of a triangle bounded by the y axis, the tine f(z) - 9 -…

A: We have to find the area of the region bounded by the y-axis, the line f(x)=9-67x, and the line…

Q: 34. Find the points where the line y = 2x intersect a circle of radius 6 centered at the origin.…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Find the points on the graph of z = xy + 8y where the tangent plane is parallel to 2x + 5y + 2z = 0.…

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Q: 5. In the standard (x, y) coordinate plane, the midpoint of LM is at (4, –4) and L is at (1,3). What…

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Q: Find the acute angles between the intersecting lines x = 2 + t, y = 4t + 2, z = 1 + t and x = 3t -…

A: Given: The equation of lines x = 2 + t,  y = 4t + 2,    z = 1 + t      and x = 3t - 2,   y = -2,   z…

Q: Find the distance from the point (1,1,5) to the line X=1+t, Y=3-t, Z=2t. O (5)^0.5 O 7 O 2(3)^0.5 O…

A: Given: Equation of line is: X = 1+ t Y = 3 - t Z = 2t To find: distance from the point (1, 1, 5) to…

Q: find √x² ds along the line of intersection of the two planes X-Y+z = 0 and x+y+ 2z =0, From origin…

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Q: (10) Find the distance of (3,-1,2) from each of the following: a) line: x = 1+ 2t, y = -t, z = 1-t…

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Q: The distance between the two lines x = 1+ t,y = -2+ 3t, z = 4 – tand x = 2s, y = s, z = s is

A: Please see the explanation below

Q: The plane given by x + y + 2z = 0 and the line given by x = 2 + t y = 1 - 2t z = 3 + t

A: The plane given by x + y + 2z = 0 and the line given by x = 2 + t;  y = 1 - 2t ;  z = 3 + t To find…

Q: Find the acute angles between the intersecting lines x = t, y = 2t, z = -t and x = 1 - t, y = 5 + t,…

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Q: The area bounded by the curve y = 4r and the lines z = 2 and I=8 above the I- aris is O 240.00…

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Q: The area (in square units) between the curve defined by y = x³, the x-axis, and the lines x = -1 and…

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Q: (c) Determine the natural cubic spline that interpolates the data f(0) = 1, f(3) = 2, f(8) = 3 and…

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Q: Find the line through (1,-1,1)and normal to the line  3x=2y=z , and parallel to the plance  x+y-z=0…

A: Equation of the line: The equation of a line passing through the point (x0, y0, z0) is given by (x,…

Q: 5) s how that the line af intersection f the Planes and 5x-2y-Z=0 is Paraliel toG Pheline X+23-22= 5…

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Q: Find the shortest distance from the origin to the line of intersection of the planes 2x + y − z = 1…

A: Given: The planes: 2x+y-z=1 and x-y+z=2.

Q: What is the sum of the abscissas of the points where the tangents of the y=(1/3) x^3-(3/2) x^2 – 2x…

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Q: An offshore oil well is located in the ocean at a point W, which is 5km from the elosest shore-point…

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Q: Find the distance from (.-4,5) to each of the following. (a) the xy-plane (b) the yz-plane (c) the…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: The area bounded by the curve y = 6z and the lines a = 5 and z= 8 above the T aris is 234.00 square…

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Q: shows an offshore oil well located at a point W that is 5 km from the closest point A on a straight…

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Q: The area bounded by the curve y = 10z and the lines z = 9,7 = 11 and a – azis is O 1010 square units…

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Q: 11. Find the distance between the point (1,0,-1) and the line x = 5 – t, y = 3 t, z = 1 + 2 t.

A: 11) The direction ratio of the lines  = -1,3,2 The direction ration of the point (1,0,-1) and the…

Q: The distance between the two lines x = 1 + t,y = -2 + 3t, z = 4 – tand x = 2s, y = s, z = s is а)…

A: Consider the provided information, x=1+t, y=-2+3t and z=4-t And, x=2s, y=s and z=s Find the distance…

Q: Which of the following straight lines are tangent to the curve y = x³ + 4x2 + 7x and passes through…

A: Topic = Geometry  y=7x ia the tangent to the curve.

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.