Find the equation of the circle which is touched by y = x has its centeron the positive direction of the x-axis and cuts off a chord of length2 units along the line \sqrt{3}y - x = 0.Prove that the pair of straight lines joining the origin to the points ofinersection of the circles x² + y² = a² and2x² + y² + 2(gx + fy) = 0 is a ² (x² + y²) - 4(x + y)² = 0.2

Since the required circle has its center on the x-axis,let the coordinates of the center be…

Find the equation of the circle which is touched by y = x has on the positive direction of the x - axis and cuts off a chord 2 units along the line \sqrt{3}y − x = 0. Prove that the pair of straight lines joining the origin to the p inersection of the circles x² + y² = a² and 2 2 x+ x² + y² + 2(gx + fy) = 0 is a² (x² + y²) - 4(x + y)² = 0.