Q 39 Equation of chord of the circle x2+y2-3x-4y-4=0 which passes through the origin such that origin divides it - Maths -

Question

Q 39 Equation of chord of the circle x 2 + y 2 - 3 x - 4 y - 4 = 0
which passes through the origin such that origin divides it in the
ratio 4 : 1, is
(a) x = 0
(b) 24x + 7y = 0
(c) 7x + 24y = 0
(d) 7x - 24y = 0

Muskaan Talwar · Accepted Answer

Dear Student,

Let equation of chord of circle be y=mx as it passes through origin
Thus, x2+y2-3x-4y-4=0⇒ x2+mx2-3x-4mx-4=0⇒1+m2x2-x3+4m-4=0Let x1, x2 be its roots
Thus, x1+x2=3+4m1+m2 and x1x2=-41+m2Since 0,0 divides the chord in ratio 4:1⇒0=4x2+x14+1⇒4x2+x1=0⇒x1=-4x2Thus we getx1+x2=3+4m1+m2 and x1x2=-41+m2⇒-4x2+x2=3+4m1+m2 and -4x2x2=-41+m2⇒-3x2=3+4m1+m2 and x22=11+m2⇒x2=3+4m-31+m2 and x22=11+m2⇒3+4m-31+m22=11+m2⇒3+4m2=91+m2⇒9+16m2+24m=9+9m2⇒7m2+24m=0⇒m7m+24=0⇒m=0 or m=-247⇒y=mx⇒y=0 or y=-247x⇒y=0 or 7y=-24x⇒y=0 or 24x+7y=0So b is correct answer

Regards

Q.39. Equation of chord of the circle x 2 + y 2 - 3 x - 4 y - 4 = 0 which passes through the origin such that origin divides it in the ratio 4 : 1, is (a) x = 0 (b) 24x + 7y = 0 (c) 7x + 24y = 0 (d) 7x - 24y = 0

Q.39. Equation of chord of the circle $x^{2} + y^{2} - 3 x - 4 y - 4 = 0$ which passes through the origin such that origin divides it in the ratio 4 : 1, is
(a) x = 0
(b) 24x + 7y = 0
(c) 7x + 24y = 0
(d) 7x - 24y = 0