Equation of the pair of tangents drawn from the origin to the circle x2+y2+2 g x+2 fy+c=0 is:

Question

Equation of the pair of tangents drawn from the origin to the circle x2+y2+2 g x+2 fy+c=0 is: (A)  g x+f y=c(x2+y2)  (B)  (g x+fy)2=x2+y2  (C)  (g x+f y)2=c2(x2+y2)  (D)  (g x+f y)2=c(x2+y2)

Tardigrade Admin · Accepted Answer

If a tangents drawn through a point (x1,y1) circles S, then the equation of pair of tangents is SS1=T2. Let S=x2+y2+2 gx+2 fy+c=0 The tangents are drawn through the origin (0, 0) to the circle is SS1=T2 ⇒ (x2+y2+2 gx+2 fy+c)c =(gx+fy+c)2 ⇒ c(x2+y2)=(gx+fy)2

Q. Equation of the pair of tangents drawn from the origin to the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ is:

$g x + f y = c (x^{2} + y^{2})$

$(g x + f y)^{2} = x^{2} + y^{2}$

$(g x + f y)^{2} = c^{2} (x^{2} + y^{2})$

$(g x + f y)^{2} = c (x^{2} + y^{2})$

Q. Equation of the pair of tangents drawn from the origin to the circle x2+y2+2gx+2fy+c=0 is:

gx+fy=c(x2+y2)

(gx+fy)2=x2+y2

(gx+fy)2=c2(x2+y2)

(gx+fy)2=c(x2+y2)

If a tangents drawn through a point (x1​,y1​) circles S, then the equation of pair of tangents is SS1​=T2. Let S=x2+y2+2gx+2fy+c=0 The tangents are drawn through the origin (0, 0) to the circle is SS1​=T2 ⇒ (x2+y2+2gx+2fy+c)c =(gx+fy+c)2 ⇒ c(x2+y2)=(gx+fy)2

Q. Equation of the pair of tangents drawn from the origin to the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ is:

$g x + f y = c (x^{2} + y^{2})$

$(g x + f y)^{2} = x^{2} + y^{2}$

$(g x + f y)^{2} = c^{2} (x^{2} + y^{2})$

$(g x + f y)^{2} = c (x^{2} + y^{2})$