A variable circle in the xy-plane is tangent to the x-axis and meets the y-axis at the points P and Q. If the circle varies in such a way that the length of the segment PQ is always 2, show that the center A of the circle lies on a hyperbola, and find the equation of this hyperbola.

The required equation of the hyperbola is y^2-x^2=1

Posted by K Sengupta on 2024-02-06 21:14:43