Question

Length of the tangent drawn from any point on the circle

x² + y² + 2gx + 2fy + c₁ = 0 to the circle

x² + y² + 2gx + 2fy + c = 0 is –

• A. $\sqrt{c_{1}–c}$
• B. $\sqrt{c–c_{1}}$
• C. $\sqrt{c_{1} + c}$
• D. None

Answer 1

Answer: (B)

$\sqrt{c–c_{1}}$

Answer 2

Let (x₁, y₁) be any point on first circle

\ $x_{1}^{2} + y_{1}^{2} + 2gx_{1} + 2fy_{1} + c_{1} = 0$ .......(i)

and also length of tangent

= $\sqrt{S_{2}}$ = $\sqrt{x_{1}^{2} + y_{1}^{2} + 2gx_{1} + 2fy_{1} + c_{1}}$

from (i) we get $\sqrt{S_{2}}$ = $\sqrt{c–c_{1}}$