Question

The equation of chord of the circle $x^2+y^2-6x-4y-12=0$ which passes through the origin such that origin divides it in the ratio 3 : 2 is

• A. y + x = 0, 7y + 17x = 0
• B. y + 3x = 0, 7y + 3x = 0
• C. 4x + y = 0, 9y + 8x = 0
• D. y + 3x = 7, y + 3x = 0

Answer 1

The correct option is A

y + x = 0, 7y + 17x = 0

Let AO = 2k, BO = 3k

Now, AO. BO = OE. OF

$k=\sqrt{2}$

Now, D is midpoint of chord AB

$AD=DB=\frac{5}{\sqrt{2}}$

Equation of AB is y = mx

$\Rightarrow \frac{|3m-2|}{\sqrt{1+m^2}}=\frac{5}{\sqrt{2}}\Rightarrow m=-1,-17/7$

Equation of AB is y = - x and y = $-\frac{17}{7}x$