Prove that x^2+y^2=a^2 and (x-2a)^2+y^2=a^2 are two equal circles touching each other. | 12 | C...

Prove that the circle x^2 + y^2 =a^2 and (x-2a)^2 + y^2 = a^2 are equal and touch each other. Also find the equation of a circle (or circles) of equal radius touching both the circles.

Show that the curves x y=a^2 and x^2+y^2=2a^2 touch each other.

Prove that the curves x y=4 and x^2+y^2=8 touch each other.

Consider the circles x^(2)+(y-1)^(2)=9,(x-1)^(2)+y^(2)=25. They are such that these circles touch each other one of these circles lies entirely inside the other each of these circles lies outside the other they intersect at two points.

Prove that the curves xy=4 and x^(2)+y^(2)=8 touch each other.

The two circles x^(2)+y^(2)=ax and x^(2)+y^(2)=c^(2)(c gt 0) touch each other, if |(c )/(a )| is equal to

Prove that the curve y^(2)=4x and x^(2)+y^(2)-6x+1=0 touches each other at thepoint (1,2), find the equation of the common tangents.

Statement 1 : The number of common tangents to the circles x^(2) + y^(2) =4 and x^(2) + y^(2) -6x - 6y = 24 is 3. Statement 2 : If two circles touch each other externally thenit has two direct common tangents and one indirect common tangent.