If the intercepts of the variable circle on the x- and y-axis are 2 units and 4 units, respectively, then find the locus of the center of the variable circle.

If the intercepts of the variable circle on the x- and yl-axis are 3 units and 6 units, respectively, then find the locus of the center of the variable circle.

The length of the intercepts on the x and y-axes of a circle are 2a and 2b unit respectively. Prove that the locus of the centre of the circle is hyperbola whose equation x^2-y^2=a^2-b^2 . Translating the origin to a suitable point show that the equation 5x^2-4y^2-20x-8y-4=0 represents a hyperbola. Find its eccentricity, coordinates of foci and equations of the directrices.

The points P and Q are on the first and third quadrant respectively and the distances of them from the x-axis and y-axis are 6 units and 4 units respectively. Find the coordinates of mid-point bar(PQ) .

A circel cuts intercepts of lenghts 2a and 2b from the x-axis and the y-axis respectively. Then the equation to the locus of the centre of the circel is-

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at Aa n dB , respectively. A variable line perpendicular to L_1 intersects the x- and the y-axis at P and Q , respectively. Then the locus of the circumcenter of triangle A B Q is

If one end of the diameter is (1, 1) and the other end lies on the line x+y=3 , then find the locus of the center of the circle.

Two rods of lengths a and b slide along the x- and y-axis , respectively, in such a manner that their ends are concyclic. Find the locus of the center of the circle passing through the endpoints.

A circle touches the x-axis and also touches the circle with centre (0,3) and radius2. The locus of the centre of the circle is

A circle is drawn to cut a chord of length 2a unit along x-axis and to touch the y-axis. Then the locus of the centre of the circle is-

From a point on the circle x^2+y^2=a^2 , two tangents are drawn to the circle x^2+y^2=b^2(a > b) . If the chord of contact touches a variable circle passing through origin, show that the locus of the center of the variable circle is always a parabola.