Explanation:
We are given the equation of a curve 3x2 - 2y2 = 6. Tangents are drawn to this curve from a point P. If these tangents intersect the coordinate axes at concyclic points, then we need to find the locus of P.

Step 1: Find the equation of the tangent to the curve at a point (x1, y1).

Differentiating the equation of the curve with respect to x, we get:

6x - 4y * dy/dx = 0
dy/dx = 3x/2y

At point (x1, y1), the slope of the tangent is given by:

m = 3x1/2y1

The equation of the tangent is given by:

y - y1 = m(x - x1)
y - y1 = (3x1/2y1)(x - x1)

Simplifying, we get:

2y1(y - y1) = 3x1(x - x1)

Step 2: Find the points of intersection of the tangent with the coordinate axes.

When the tangent intersects the x-axis, y = 0. Substituting this in the equation of the tangent, we get:

2y1(-y1) = 3x1(x - x1)
x = x1 - (2y1/3)(y1)

When the tangent intersects the y-axis, x = 0. Substituting this in the equation of the tangent, we get:

2y1(y - y1) = 3x1(-x1)
y = y1 - (3x1/2)(x1)

Step 3: Find the condition for the points of intersection to be concyclic.

Let the points of intersection be (a, 0), (0, b), (-a, 0), and (0, -b). These are the four points of a rectangle with sides parallel to the coordinate axes.

The condition for these points to be concyclic is:

(a - 0) * (0 + b) + (0 - (-a)) * (b + 0) + (-a - 0) * (0 - b) + (0 - 0) * (-b - 0) = 0
ab - ab - ab - ab = 0
-4ab = 0

This implies that either a = 0 or b = 0.

Step 4: Find the locus of P.

If a = 0, then the points of intersection are (0, b), (0, -b), and (-x1, y1) (since x = x1 - (2y1/3)(y1) and y = y1 - (3x1/2)(x1) both cannot be zero). This implies that P lies on the y-axis.

If b = 0, then the points of intersection are (a, 0), (-a, 0), and (x1, y1) (since x = x1 - (2y1/3)(y1) and y = y1 - (3x1/2)(x1) both cannot be zero). This implies that P lies on the x-axis.