If the length of the tangent from any point on the circle (x-3)²+(y+2)²=5 r² to the circle (x-3)²+(y+2)²=r² is 16 units, then the area between the two circles in sq units is

Step-by-step solution

Let point P (x₁, y₁ ) be any point on the circle, therefore it satisfy the circle (x₁-3 )²+ (y₁+2 )²=5 r²...(i) The length of the tangent drawn from point p (x₁, y₁ ) to the circle (x-3)²+(y+2)²=r² is (x₁-3 )²+ (y₁+2 )²-r² = 5 r²-r² = 4 r² =2 r 2 r=16 r=8 So, area between two circles aligned &= (5 r² )- r² &=5 r²- r² &=4 r²=4 64 &=256 sq units aligned