If a circle S₂ lies completely inside the circle S₁= 0, then the locus of the center of a variable circle S=0 that touches both the circles is an ellipse . Assertion Locus of the center of a variable circle touching two circles (X-1)²+(Y-2)² = 25 and (X-2)²+(Y-1)²=16 is an ellipse?
a) both statement 1 and statement 2 are correct and statement 2 is the correct explanation for statement 1
b) both statement 1 and statement 2 are correct but statement 2 is not the correct explanation for statement 1
c) statement 1 is correct but statement 2 is incorrect
d) statement 1 is incorrect but statement 2 is correct