The length of the tangent drawn from any point on the circle x2+y2+2 g x+2 f y +c1=0 to the circle x2+y2+2 g x+2 f y+ c2=0 is

Question

The length of the tangent drawn from any point on the circle x2+y2+2 g x+2 f y +c1=0 to the circle x2+y2+2 g x+2 f y+ c2=0 is (A) √c2-c1 (B) √c12-c22 (C) c1+c2 (D) c2-c1

Tardigrade Admin · Accepted Answer

Circles are C1 ≡ x2+y2+2 g x+2 f y +c1=0 and C2 ≡ x2+y2+2 g x+2 f y+ c2=0 Clearly circles are concentric, <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/379035bedba51185a6ef6819950fa1d4-.png" /> Cleariy, length of tangent is AT =√ AO 2- OT 2=√r1 2-r2 2 =√(g2+f2-c1)-(g2+f2-c2) =√c2-c1

Q. The length of the tangent drawn from any point on the circle $x^{2} + y^{2} + 2 gx + 2 f y + c_{1} = 0$ to the circle $x^{2} + y^{2} + 2 gx + 2 f y + c_{2} = 0$ is_____

$c_{2} - c_{1}$

$c_{1}^{2} - c_{2}^{2}$

$c_{1} + c_{2}$

$c_{2} - c_{1}$

Q. The length of the tangent drawn from any point on the circle x2+y2+2gx+2fy+c1​=0 to the circle x2+y2+2gx+2fy+c2​=0 is_____

c2​−c1​​

c12​−c22​​

c1​+c2​

c2​−c1​

Circles are C1​≡x2+y2+2gx+2fy+c1​=0 and C2​≡x2+y2+2gx+2fy+c2​=0 Clearly circles are concentric, Cleariy, length of tangent is AT=AO2−OT2​=r1​2−r2​2​ =(g2+f2−c1​)−(g2+f2−c2​)​ =c2​−c1​​

Q. The length of the tangent drawn from any point on the circle $x^{2} + y^{2} + 2 gx + 2 f y + c_{1} = 0$ to the circle $x^{2} + y^{2} + 2 gx + 2 f y + c_{2} = 0$ is_____

$c_{2} - c_{1}$

$c_{1}^{2} - c_{2}^{2}$

$c_{1} + c_{2}$

$c_{2} - c_{1}$