Question

Find the equation of the circle whose diameter
is the common chord of the circles
s'=x² + y2 + 2x+3y+1=0 and
s' = x² + y2 + 4x + 3y + 2 = 0​

Answer 1

S ≡ x2 + y2 + 2x + 3y + 1 = 0 —— (1)  S' ≡ x2 + y2 + 4x + 3y + 2 = 0 —— (2)  Here the common chord is the radical axis of (1) and (2).  The equation of the radical axis is S – S′ = 0.  i.e., 2x + 1 = 0 —— (3)  The equation of any circle passing through the points of intersection of (1) and (3) is (S + λL = 0) (x2 + y2 + 2x + 3y + 1) + λ(2x + 1) = 0  x2 + y2 + 2(λ + 1)x + 3y + (1 + λ) = 0 — (4) The centre of this circle is (− (λ + 1), 3/2).  For the circle (4), 2x + 1 = 0 is one chord. This chord will be a diameter of the circle (4) if the centre of (4) lies on (3).  ∴ 2{–(λ + 1)} + 1 = 0  ⇒ λ = – 1/2  Thus equation of the circle whose diameter is the common chord (1) and (2) [put λ = 1/3 in equation (4)]  2(x2 + y2) + 2x + 6y + 1 = 0 ← Prev QuestionNext Question → Related questions 0 votes 1 answer Find the equation of the circle whose diameter is the common chord of the circles (x − a)^2 + y^2 = a^2 and x^2 + (y − b)^2 = b^2. asked Oct 28, 2019 in Mathematics by SudhirMandal (53.5k points) circle 0 votes 1 answer If ax + by + c = 0 is the equation of the common chord of the circles 3x^2 + 3y^2 - 2x + 12y – 9 = 0 asked Oct 30, 2019 in Mathematics by RiteshBharti (53.8k points) circle 0 votes 1 answer Find the equation of the circle described on the common chord of the circles x^2 + y^2 - 4x – 5 = 0 and x^2 + y^2 + 8y + 7 = 0 as diameter asked May 2, 2019 in Mathematics by Bhawna (68.5k points) circles jee jee mains 0 votes 1 answer Length of common chord of the circles x^2 + y^2 + 2x + 3y + 1 = 0 and x^2 + y^2 + 4x + 3y + 2 = 0 is (1) 9/2 asked Nov 20, 2018 in Mathematics by aditi (75.7k points) intersection of two circles jee jee mains 0 votes 1 answer Find the equation of the described on the common chord of the circles (x − a)^2 + y^2 + a^2 and x^2 + (y − b)^2 + b^2 as diameter. asked Oct 28, 2019 in Mathematics by SudhirMandal (53.5k points) circle Read more on Sarthaks.com - https://www.sarthaks.com/535929/find-the-equation-of-the-circle-whose-diameter-is-the-common-chord-of-the-circles-x-2-y-2-2x-3y