The distance between the chords of contact of tangents to the circle x2+y2+2 g x+2 f y+c=0 from the origin and from the point ( g , f ) is -

Question

The distance between the chords of contact of tangents to the circle x2+y2+2 g x+2 f y+c=0 from the origin and from the point ( g , f ) is - (A) √ g 2+ f 2 (B) (√ g 2+ f 2- c /2) (C) ( g 2+ f 2- c /2 √ g 2+ f 2) (D) (√ g 2+ f 2+ c /2 √ g 2+ f 2)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/5c9e825b0bca583477c58ce93e406770-.png" /> Equation of AB: gx +f y + c =0 ldots ldots..(i) Equation of CD: gx +f y + g ( x + g )+f( y +f)+ c =0 gx +f y +( g 2+f2+ c /2)=0 text .....(ii) Distance between AB CD will be |((g2+f2-c/2)/√g2+f2)|=(g2+f2-c/2 √g2+f2)

Q. The distance between the chords of contact of tangents to the circle $x^{2} + y^{2} + 2 gx + 2 f y + c = 0$ from the origin and from the point $(g, f)$ is -

$g^{2} + f^{2}$

$\frac{g ^{2} + f ^{2} - c}{2}$

$\frac{g ^{2} + f ^{2} - c}{2 g ^{2} + f ^{2}}$

$\frac{g ^{2} + f ^{2} + c}{2 g ^{2} + f ^{2}}$

Q. The distance between the chords of contact of tangents to the circle x2+y2+2gx+2fy+c=0 from the origin and from the point (g,f) is -

g2+f2​

2g2+f2−c​​

2g2+f2​g2+f2−c​

2g2+f2​g2+f2+c​​

Equation of AB:gx+fy+c=0……..(i) Equation of CD:gx+fy+g(x+g)+f(y+f)+c=0 gx+fy+2g2+f2+c​=0.....(ii) Distance between AB & CD will be ∣∣​g2+f2​2g2+f2−c​​∣∣​=2g2+f2​g2+f2−c​

Q. The distance between the chords of contact of tangents to the circle $x^{2} + y^{2} + 2 gx + 2 f y + c = 0$ from the origin and from the point $(g, f)$ is -

$g^{2} + f^{2}$

$\frac{g ^{2} + f ^{2} - c}{2}$

$\frac{g ^{2} + f ^{2} - c}{2 g ^{2} + f ^{2}}$

$\frac{g ^{2} + f ^{2} + c}{2 g ^{2} + f ^{2}}$