A point moves such that the ratio of its distances from two fixed point is constant, show that its locus is a sphere.

Q: (6) Let -1 3 1 y = 2 and uj = -1 u2 -1 -2 Find the closest point to y in span{u1,u2}. What is the…

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Q: Represent two planes that intersect at a line represented by 3. y- 7 = z+2 2.

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Q: Find the coordinates of a rectangle with corner points at A: (2,4), B:(2,8), C: (5,8), and D: (5,4),…

A: We have to find co-ordinate after translating 6 units up and 2 units left

Q: how that the point (1,0,-1) is the centre of the sphere passing through…

A: Let O=(1,0,-1), A=(1,8,-8) B=(-9,0,5) C=(7,-8,-1) D=(-7,0,7) It is enough to show that…

Q: 9 Find the distance from the point (-7,-3,4) to the xy-plane.

A: Distance of a point (a,b,c) from the plane lx+my+nz=p is (la+mb+nc-p)/sqrt(l^2+m^2+n^2)

Q: A variable straight line is drawn through the point of intersection of the straight lines x/a+y/b=1…

A: Given lines arexa+yb=1               ....(1)and  xb+ya=1               ....(2)Solving (i)and(ii) we…

Q: Suppose a triangle has the following vertices: v1 = (-2, 3, 6) v2 = (4, 5, -1) v3 = (3, 3, 0) What…

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Q: Give a parametric representation for the straight line segment from the point (1,-1,2) to the point…

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Q: What is the distance between the origin and the point (4, 3, 3)

A: To find the distance between the origin and the point (4, 3, 3)

Q: Points A = (−5, 12, 0) and B = (13, 0, 0) are on the sphere x2 + y2 + z2 = 132. Find the distance…

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Q: What is the dual of the phrase “three collinear points and a fourth point not on the line of the…

A: Answer :  Dual of any phrase can be find by replacing the conjunction connective with disjunction…

Q: Quadrilateral ABCD is defined by points A = (-2,1), B = (0,0), C = (3, 1/2), and D = (x4, y4). If…

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Q: the midpoint of line segment with end points (-1,6,2) and (3, 2, -4) What is the distance between B…

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Q: ind point P and Q on the parabola y=(-x^2)+1 so that the triangle ABC formed by the x-axis and the…

A: Given that the curve is                         To find point P and Q on the given parabola, so that…

Q: What is the distance from the point (1,9,3) to the xz-plane?

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Q: The following line intersect with the xz-plane. What is the point? x = -2; y = 4+2λ; z = −3+2

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Q: What are the coordinates of the top point of an equilateral triangle if the corners of its base are…

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Q: In two-dimensional Euclidean space, consider a curve defined by the equation x^2 + y^2 - 6x + 4y -…

A: In this question, we are provided with a quadratic equation in two variables x and y. In a…