A point moves so that the ratio of its distances from 3x + 4y + 8 = 0 and 4x + 3y – 6 = 0 is 2. Find the equation of its locus.

Q: Find the abscissa of the point on the graph of y=V 2x – 1 that is parallel to the line 2x - y+1=0

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Q: b. Enclosed by the curves y² = 4x + 4 and the line y = 4x – 16.

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Q: 4. Find the equation of the locus of the points P(x, y) whose distances from the point (3,2) are…

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Q: * the lines 2x 3y 1 0 and 3x y 4 0 ie along diameters of a circle of circumference 10 n, then the…

A: The equation of a circle centered at h,k is x-h2+(y-k)2=r2 , where, r is the radius. If the radius…

Q: Find the coordinates of the intersection points A and B, between the closed curve (x + 1)² + 4(y-1)²…

A: In this question, we can find the intersection points of the given curve. Using the equation of…

Q: Sketch the lines 3x+ 4y 7 and x- 2y = 6, and find their point of intersection. Hint: Their point of…

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Q: Find the equation of the family of curves whose at any point (X, Y) is 1. 3x? + 4 2. * y X+1 3. y-1…

A: Here, there is a little word missing in sentence, 'Find the equation of family of curves whose slope…

Q: Find the length of the curve y = x2, 0 ≤ x≤√3/2.

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Q: Which of the following lines passes through the point (3, –7) and is perpendicular to the line whose…

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Q: The point (a,b) and (c,d) are points on the graph of y= x3+5 whose tangent lines are perpendicular…

A: y=x3+5slope at a,b =2x2=2a2     ...(1)slope at c,d =2x2=2c2     ...(2)slope of given line = -13…

Q: parallel

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Q: Show that the locus of the point whose distance from y-axis is thrice it's distance from (1,2,-1) is…

A: The equation of the ellipse is 8x2+9y2+8z2+18x-36y+18z+54=0 The locus of the point whose distance…

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Find the equation for the set of points in an xy-plane that are equidistant from the point P -6,3…

Q: Find all points having a y-coordinate of - 3 whose distance from the point   (1, 2) is 13.

A: Consider the points are A = (x,-3) and B=(1,2) The distance between A and B is 13 units.   If the…

Q: Find the length of the curve: x3 1 y = - 3 4x' 1<x< 3

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Q: The graph of the curve described by the paramnetric equations x = 3t – 4, y = 6t + 2 is a straight…

A: Consider the curve  x=3t-4,y=6t+2

Q: Find the point(s) of intersection of the parabola y =x2+ 2 andthe line y = x + 4.

A: The given functions are y=x2+2   and   y=x+4

Q: * the lines 2x . 3y 1=0 and 3x - y -4 = 0 ke along diameters of a circle of circumference 10 , then…

A: The equation of a circle centered at h,k is defined by the equation, x-h2+y-k2=r2, where r is the…

Q: Sketch parallelogram-INDY with diagonals intersecting at point P in the box below on the left. If IP…

A: Given,           A parallelogram INDY with diagonals intersevting at point P.           IP=3x,…

Q: Find the point where the common point of the circles x2+y2=25 and x2 +y2-12x-6y+35=0 intersects…

A: This is coordinate geometry problem

Q: Find the point on the line y = 3x + 5 that is closest to the origim %3D (x, y) = %3D

A: We have to solve

Q: The equation of the line tangent to the intersection of two surfaces 2 = a2 and z 25- y? at the…

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Q: Show that the locus of the point whose distance from Y-axis is thrice its distance from (1,2,-1 ) is…

A: First of all we will suppose an arbitrary point and then try to find its locus using the given…

Q: The point that is symmetric with respect to the x-axis to the point (2,-5) is _____.

A: The point that is symmetric with respect to the x axis to the point (2,-5) is be found with the help…

Q: |xy dA, D is enclosed by the quarter-circle 20. y - 1 - x² , x > 0, and the axes

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Q: Find an equation of the line containing the centers of the two circles x2 + y2 + 2x + 2y + 1 = 0 and…

A: Given,

Q: Find the equation of the set of points which are equidistant from (3,10) and the x-axis `y-x -5)²+3…

A: To find the correct option

Q: (i) Find the equation of the circle passing through (0,0) and making intercepts 4,3 on X-axis and…

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Q: shows the image of (D2 • Ry-axis)(4, -3)?

A: D2∘Ry-axis4,-3 this means 4,-3will be reflected over the y-axis. And then it will be dilated by 2.…

Q: Find the equation of bisector of the acute angle between the lines 3x – 4x + 7=0 and 12x + 5y – 2 =…

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Q: Find the point on the x-axis that is equidistant from the points (1, 2) and (2, 3). The coordinates…

A: soln:point on x-axis which is equidistant from the points 1,2 and 2,3

Q: The equation of the line that goes through the point (1,1) and is perpendicular to the line 4x+4y=4…

A: Given,           The equation of the line that goes through the point (1,1) and is perpendicular to…

Q: Draw a diagram showing two perpendicular lines that intersecton the -axis and are both tangent to…

A: The given parabola equation , y=x2. To draw two perpendicular lines that intersect on the axis and…

Q: find the equation of the locus of a point that moves so as to be always equidistant from A(3,4) and…

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Q: Find the equation of locus of a point P such that the distance of P from the origin is twice the…

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Q: Find the equation of the set of all points that are equidistant from the points P = (1,0, -2) andQ =…

A: Given: P=1,0,-2 and  Q=5,2,4

Q: Show that the locus of the point whose distance from Y-axis is thrice it's distance from (1,2,-1) is…

A: Let the arbitrary point be Px,y,z. Consider that the distance between two points is given by the…

Q: The length of the line segment joining the two points of intersection is 3 – x = y = 7+1 With the…

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

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Q: i) Find the exact length of the curve x5 1 15 4x3 y= + 1 < x < 2,

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Q: Consider the two points (4,2) and (10,4). The distance between them is:   The x co-ordinate of the…

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Q: Find equation of the line Passes through the Peint (-3,2,-1)-and parallel te the lineof intersection…

A: Given that: The given point is: (-3, 2, -1)The planes are: π1: x+2y+z=8 and π2:x+y-z=2

Q: A curve C has equation y =x2lnx- 2x +5, x > 0. %3D For which values of x, the curve C is convex?

A: The equation of the given curve is  y=13x2 ln x-2x+5 , x&gt;0 For the curve to be convex its second…

Q: * the lines 2x • 3y + 1 = 0 and 3x - y - 4 = 0 ke along diameters of a circle of circumference 10 n,…

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Q: Find the locus of the points that are equidistant to the point F (0,2) and the line y=-2

A: Use distant formula..

Q: Show that the locus of the point whose distance from Y-axis is thrice it's distance from (1,2,-1) is…

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Q: The length of the curve 4/2 3 y = xi - 1,0 < x < 1 is .

A: Given,            The length of the curve y=423x32-1 , 0≤x≤1 is 136.To find : Check whether the…

Q: Find the equations of the line through (2,0, –4) and parallel to each of the planes x + y – z = 0…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.