Which of the following equations describes all points that are 6 unlts away from th point (-2, 4)? A (x + 2)2 + (y - 4)2 = 6 %3D B (x- 2)2 + (y + 4)2 = 62 %3D C (x + 2)2 + (y- 4)2 62 %3D

Q: Find a relationship between x and y such that (x, y) is equidistant the same distance from the two…

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Q: If A ABC is reflected across the line y-z+ 1, what are the coordinates of Point A post-reflection?…

A: In the question it is asked to show the reflection of the triangle shown in figure. It is asked to…

Q: Find k so that the line through (4, -1) and (k, 2) is a. parallel to 2x + 3y = 6, b. perpendicular…

A: The line passes through the points (4, -1) and (k, 2). Then the slope (m) of this line is: m = [2 -…

Q: Explain how you can find the coordiantes of a point 1/8 of the way from point A to point B.

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Q: The plane through the points (-4,-8,-1), (8,3,5), (7,8,6) has equation Ax + By + Cz= D. If A = - 19…

A: Since plane passes through the given points therefore

Q: 6. Find the symmetric equation of the line parallel to ở = (1,4, 6) + t(−2, 4, 7) that intersects…

A: Given problem:- 6. Find the symmetric equation of the line parallel to r = (1,4,6) + t(−2, 4, 7)…

Q: The coordinates of a particle change by Δx = 5 and Δy = 6 as itmoves from A(x, y) to B(3, -3). Find…

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Q: What are the coordinates of (-4, 1) after a reflection over the y-axis? 10- 8- 6+ 4+ (-6, 1) (-4, 1)…

A: Given, The coordinates of point -4, 1  We have to find the coordinates of point -4, 1 after a…

Q: Find the coordinates of the point which divides the line segment connecting (-1,4) and (2,-3) into…

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Q: What is the vertex of y = Vx + 4+1 O (4, -1) O (4, 1) O (-4, 1) O (-4, -1)

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Q: 3) Point R bisects XY. If XR=4n and YR=6n-9, what is the length of XY?

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Q: The X- coordinate of a point P is twice it's y-coordiante ,If P is equidistance from Q(2,-5)…

A: To find the coordinate of P

Q: Find the symmetric equation of line L, that passes through the points (1, 8, 9) and (5, 9, 0).…

A: 9

Q: Imeter) Y ( meter) POINT 1 1254,72 2951,76 2 1362,50 3205,13 3 1578,94 3713,80 4 1843,68 4335,92

A: A table of data is given, and the general equation of a line is y=ax+b. Here, a is the slope, and b…

Q: Which equations below are parallel to the line 6x - 9y = 36 a. 2x = 3y b. 2у 3D 3х +24 2x + 3y = 0…

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Q: 9. Find a point on the y-axis which is equidistant from the point A (6,5) and B (-4,3).

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Q: Identify the new coordinates of (-4, 1) after a reflection across the y-axis. y 10- 8- 6- 4+ ((6, 1)…

A: Given  Coordinate (-4,1)

Q: 7. How many points of intersection exist between y= x' +4x2- 2x - 5 and y = 3? %3D None B. One Two…

A: To find the number of intersection of the given curves  y = x3 + 4x2 - 2x -5  and y = 3

Q: what about a point? horizontally point vertically to the point If F(x, y, z) = 2x² + xyz – y²z What…

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Q: find the distance from the point (−5, 1) to the line 3x − 4y + 1 = 0.

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Q: Find the distance between u = 0 - 4 and z = 3 - 3 - 1 8

A: The distance between two vectors u=a1a2a3 and v=b1b2b3 is: d=b1-a22+b2-a22+b3-a32 The distance…

Q: Find k so that the line through (-3,5) and (k,8) is a) parallel to 5y-3x 8; b) perpendicular to 3y +…

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Q: 1)calculate xy dady Where D is a triangle with vertices (0,0), (5,0) and (5,5) tip:Don't use the…

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Q: Find the relationship between x and y such that point (x,y) is equidistant from the points (7,1) and…

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Q: The distance between the points A= (-4,-2) and B= (4,4) is O V217 units O V41 units O v65 units O…

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Q: Predict the location of the endpoints of the image when you dilate the preimage by a scale factor…

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Q: 4. A (-3, 1) 5. P(4,-3) and М(2, 2) Q(-1,4) and

A: The points are:4) A-3, 1 and M2, 25) P4, -3 and Q-1, 4To find the distance between them.

Q: What are the coordinates of (-4, 1) after a reflection over the y-axis? 10- 8- 6+ (-6, 1)(-4, 1)2+ 4…

A: Given,  The coordinates of point -4, 1  We have to write the coordinates of point -4, 1 after a…

Q: 3. Find the point (x1, x2) that lies on the line x + 5x2 = 7 and on the line x1 – 2x2 = -2. See the…

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Q: Verify that ARST ~ AXYZ. Find the scale factor of ARST to AXYZ. 5. 6 6. X, 16 Y 12 28 21

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Q: The distance from a point P₁(x1, y₁) to the line ax + by + c = 0 is lax₁ + by₁ + cl √² + b² Use this…

A: SOLUTION-

Q: d the condition for the point (a,0),(h,k),(0,b) when ab is not equal to 0 to be collinear

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Q: What are the coordinates of latera recta of the equation 16x² + 9y² + 64x – 18y-71= 0? 17 17 ,1+. 1…

A: Given query is to find the coordinates or latera recta of the equation.

Q: Suppose W(8, -2) was transformed across the line y = -x. What is the y coordinate for the image of…

A: I have stated the used formula in the solution

Q: 5. Find the point of intersection of the following lines x = 4t +2, y = 3, z = -t +2 b. x = 2s +6, y…

A: Given query is to find the point of intersection of line a and line b.

Q: an object is traveling on a path of y=sprt(x+3) where will the object be closest to (2,0)

A: We have to find the closet point to (2, 0)

Q: Find the distance between the point (-2, 4) and the point of origin. * O 4 O 2v5 O 5v2 O 5

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Q: Scalar line integrals Evaluate the following line integral along the curve C.

A: Given:  where, C is the line segment from (-1,0) to (0,1) followed by the line segment from (0,1)…

Q: distance between (0, 0) and (½a, ½a√3)

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Q: The equation for the set of all points (x, y) that are equidistant from the points (-1,2) and (3,-2)…

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Q: The plane through the points (-2,2,-1), (7,6,4), (-3,-4,1) has equation Ar + By + Cz = D. If A 38…

A: In this question , we can find the value of B ,C,D .As plane passing through the given points. So…

Q: Find all yy such that the distance between the points (3, -8) and (-10, yy) is 19

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Q: 18x, x=2, AOR = X-AXIS

A: Topic:- application of integration

Q: Find the coordinates of the image. Ry-axis (S) -3 -3- th

A: From the graph given point S is at (3,6) Now reflect the point S across y axis For reflection across…

Q: Find the value of k such that the perpendicular distance of the point (2,k) from the line x - 2y =…

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Q: The plane through the points (2,-7,-8), (7,1,1), (4,6, 2) has equation Ar + By + Cz= D. If A -69…

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Q: 4) Find the two points of the form (x,-4) that have the same distance of 10 units from the point…

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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.