If the length of the tangent from (h, k) to the circle x^2+y^2=16 is twice the length of the tangent from the same point to the circle x^2+y^2+2 x+2 y=0 , then

Step-by-step solution

Given equations of circle is x^2+y^2=16 and x^2+y^2+2 x+2 y=0 According to the questions, Length of the tangent from (h, k) to the circle x^2+y^2=16 =2 Length of the tangent from (h, k) to the circle x^2+y^2+2 x+2 y=0 h^2+k^2-16 =2 h^2+k^2+2 h+2 k On squaring both sides, we get aligned & h^2+k^2-16=4 (h^2+k^2+2 h+2 k ) & 3 h^2+3 k^2+8 h+8 k+16=0 aligned