What is locus?

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What is the locus of the equations x^2+y^2+z^2=0 ?

Show that the locus of the point of intersection of mutually perpendicular tangetns to a parabola is its directrix.

Prove that the locus of a point that is equidistant from both axis is y=x.

Prove that the locus of the centroid of the triangle whose vertices are (acost ,asint),(bsint ,-bcost) and (1,0) , where t is a parameter, is circle.

Having given the bases and the sum of the areas of a number of triangles which have a common vertex, show that the locus of the vertex is a straight line.

If on a given base B C , a triangle is described such that the sum of the tangents of the base angles is m , then prove that the locus of the opposite vertex A is a parabola.

If the sum of the distances of a variable point from two perpendicular lines in a plane is 1, then its locus is :

Show that the locus of the middle points of chord of an ellipse which paas through a fixed point, is another ellipse

Show that the locus of the point, the powers of which with respect to two given circles are equal, is a staight line.

Show that the locus of a point that divides a chord of slope 2 of the parabola y^2= 4x internally in the ratio 1 : 2 is a parabola. Find the vertex of this parabola.

What is locus?

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