The locus of the centre of a circle the touches the given circle externally is a _______

Prove that the locus of the center of the circle which touches the given circle externally and the given line is a parabola.

Two circles are given such that they neither intersect nor touch. Then identify the locus of the center of variable circle which touches both the circles externally.

Prove that the locus of centre of the circle which toches two given disjoint circles externally is hyperbola.

The locus of the centres of the circles, which touch the circle, x^(2)+y^(2)=1 externally, also touch the Y-axis and lie in the first quadrant, is

The locus of the centre of a circle which touches the circle |z-z_(1)|=a " and "|z-z_(2)|=b externally (z, z_(1)" and "z_(2) are complex numbers) will be

Consider the locus of center of the circle which touches the circle x^(2)+y^(2)=4 externally and the line x=4. The distance of the vertex of the locus from the otigin is __________ .

Find the locus of the center of the circle touching the circle x^2+y^2-4y=4 internally and tangents on which from (1, 2) are making of 60^0 with each other.

Two circles are given such that one is completely lying inside the other without touching. Prove that the locus of the center of variable circle which touches the smaller circle from outside and the bigger circle from inside is an ellipse.

The locus of the centre of a circle which touches externally the circle x^2 + y^2-6x-6y+14 = 0 and also touches Y-axis, is given by the equation (a) x^2-6x-10y+14 = 0 (b) x^2-10x-6y + 14 = 0 (c) y^2+6x-10y+14-0 (d) y^2-10x-6y + 14 = 0

Statement 1 : The locus of the center of a variable circle touching two circle (x-1)^2+(y-2)^2=25 and (x-2)^2+(y-1)^2=16 is an ellipse. Statement 2 : If a circle S_2=0 lies completely inside the circle S_1=0 , then the locus of the center of a variable circle S=0 that touches both the circles is an ellipse.