CircleHard
Question
If the two circles, x2 + y2 + 2g1x + 2f1y = 0 and x2 + y2 + 2g2x + 2f2y = 0 touches each other, then -
Options
A.f1g1 = f2g2
B.
C.f1f2 = g1g2
D.none
Solution
C1C2 = r1 + r2
⇒ (g1 - g2)2 + (f1 - f2)2 =
⇒ -2g1g2 - 2f1f2 = ± 2
⇒ g1f2 - g2f1 = 0
⇒
⇒ (g1 - g2)2 + (f1 - f2)2 =
⇒ -2g1g2 - 2f1f2 = ± 2
⇒ g1f2 - g2f1 = 0
⇒
Create a free account to view solution
View Solution FreeMore Circle Questions
Through the vertex ′O′ of the parabola y2 = 4ax, variable chords OP and OQ are drawn at right angles. If the...Consider the circle x2 + (y − 1)2 = 9, (x − 1)2 + y2 = 25. They are such that-...An equilateral triangle OAB is inscribed in the parabola $y^{2} = 4x$ with the vertex O at the vertex of the parabola. T...Let $y = x$ be the equation of a chord of the circle $\mathbf{C}_{1}$ (in the closed half-plane $x \geq 0$ ) of diameter...If y = c is a tangent to the circle x2 + y2 − 2x + 2y −2 = 0 at (1, 1), then the value of c is-...