A circle cuts intercepts of length 2a unit and 2b unit from the x-axis and y -axis respectively. Show that the locus of the centre of the circle is `x^(2)-y^(2)=a^(2)-b^(2)`.

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-

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-

A rod of length a unit slides on the x-axis and another rod of length b unit slides on the y-axis in such a way that the four extremities of the rod are concylic. Show that the locus of the centre of the circle is 4(x^(2)-y^(2))=a^(2)-b^(2) .

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.

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.

A circle of radius r passes through the origin and intersects the x-axis and y-axis at P and Q respectively. Show that the equation to the locus of the foot of the perpendicular drawn form the origin upon the line segment bar (PQ) is (x^(2)+y^(2))^(3)=4r^(2)x^(2)y^(2) .

Find the locus of the center of the circle which cuts off intercepts of lengths 2a and 2b from the x-and the y-axis, respectively.

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

Find the equation of a circle through origin which cuts of intercepts -2 and 3 units from the x-axis and Y-axis respectively.