Find the equation of locus of a point P such that the distance of P from the origin is twice the distance of P from A (1,2).

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: Determine the angle between the curves 2x=y2 and x2+y2-5x=0

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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 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: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

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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: Find a plane containing the point (7,-8,8) and the line F(t) = +t

A: Given that, the point is 7,-8,8 and the line is r→t=-6,-8,-7+t6,8,4. From the given line, the point…

Q: the Find the distance bebween point of inter Section of the Line %3D X -y -Z =2, 2 x +34 -7Z = -1 |…

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Q: Find the equation of the locus of the center of the circle which moves so that it is tangent to the…

A: Find equation of locus :

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: Find the distance from (4, –2, 6) to each of the following. a. The xy-plane

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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: . If a point P is moving such that the lengths of tangents drawn from P to the circles x² + y² +8x…

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Q: b. Find the distance from the point (2, –2, 3) to the intersection of the planes 2x – y + 3z = 1 and…

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Q: Find an equation for the set of points P(x, y) in a plane the sum of whose distances from two fixed…

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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: Prove that the curves x2−y2=3 and xy=2 intersect at the right angle.

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Q: Suppose that P is twice as far from (0, 0) as P is from (6, 0 Find such a point on the x-axis.

A: Let A0,0 and B6,0. It is given that P is twice as far from A0,0 as from B6,0. We know that if point…

Q: Find the locus of the points P(x, y) such that PA = 2PB where A is the point with coordinates (0, 3)…

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Q: 2 =(x² - 1)³/²,1 ≤ x ≤ 3

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Q: Find all planes in R^3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.

A: To find all planes in ℝ3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.…

Q: Find a plane containing the point (-3,3,-3) and the line F(t) = +t

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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: Show the symmetry tests for the curve r=3-3costheta

A: Consider the curve

Q: Find the Cartesian equation of the locus of points satisfying PA + PB = 12, where A is the point…

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Q: Find the length of the curve y=x^3/2 from (1,1) to (2,2squareroot2)

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Q: Prove that the curves y2 = 4x and y2-6x+1 = 0 touch each other at the point (1,2)

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Q: 1. Determine the equation of the locus of the point which moves so that the sum of its distances…

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Q: Find the midpoint of points A(-9, 7) and B(1, 10) graphically. Plot the line segment AB by clicking…

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Q: Sketch the locus of points P(x, y) and write down its Cartesian equation given that P is equidistant…

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Q: Prove that the curves y2 = 4x and x2+ y2-6x+1 = 0 touch each other at the point (1,2)

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Q: 8) Determine if the line given by r(t) = intersects the xz-plane. If so, determine at what point.

A: we have to find the point of intersection.

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 number  a such that the line x = a  bisects thearea under the curve  y = 1 / x 2  , 1<…

A: Our Aim is to find a number such that line x=a bisects the area under the curve y=1x2, 1≤x≤4.

Q: sketch the curve r=1-3costheta

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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 relation between x and y such that the point (x,y) is equidistant from the points (7,1) and…

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Q: the

A: We will find the distance.

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: Q1) Find the locus of the points that are equidistant to the point F(0,2) and the line y = -2. A) y²…

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

A: Let us consider that, an arbitrary point P is x,y. Vertices of origin and point A are 0,0 and 1,2…

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: (A) Find the unique point P on the y-axis which is on both planes. (–, ,

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

Q: Give the Cartesian equation of the locus of points P(x, y) given that P is 5 units from the point…

A: Any point on the Cartesian plane is represented as x, y. The locus is a set of points on the…

Q: A curve on the ry-plane passes through the point (0, a) for some number a, and has the property that…

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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: Find the paths orthogonal to the family of curves: cy ^ 2 = xe ^ x

A: Orthogonal path is a curve if it cuts every member of a given family of curves at right angles.

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.