A chord of the circle x2 + y2 4x 6y = 0 passing through origin subtends an angle tan -1 (7/4) at the point where the

Question

A chord of the circle $x^{2} + y^{2} - 4 x - 6 y = 0$ passing through origin subtends an angle $\tan^{- 1} (\frac{7}{4})$ at the point where the circle meets positive $y$ -axis, then equation of the chord is

Smart Achievers · Accepted Answer

(3)

$Equation of tangent at origin is$

$- 2 (x + 0) - 3 (y + 0) = 0 \Rightarrow 2 x + 3 y = 0$

$\tan θ = \frac{7}{4} \Rightarrow$ $| \frac{m + \frac{2}{3}}{1 - \frac{2 m}{3}} |$ $= \frac{7}{4} \Rightarrow \frac{3 m + 2}{3 - 2 m} = \frac{7}{4}$

$\Rightarrow 12 m + 8 = 21 - 14 m \Rightarrow 26 m = 13 \Rightarrow m = \frac{1}{2}$

$∴$ $y = \frac{1}{2} x \Rightarrow x - 2 y = 0$

Solution

Q.
A chord of the circle $x^{2} + y^{2} - 4 x - 6 y = 0$ passing through origin subtends an angle $\tan^{- 1} (\frac{7}{4})$ at the point where the circle meets positive $y$ -axis, then equation of the chord is

1 $2 x + 3 y = 0$

2 $x + 2 y = 0$

3 $x - 2 y = 0$

4 $2 x - 3 y = 0$

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Solution

Q. A chord of the circle x2+y2-4x-6y=0 passing through origin subtends an angle tan-1(74) at the point where the circle meets positive y-axis, then equation of the chord is

1 2x+3y=0

2 x+2y=0

3 x-2y=0

4 2x-3y=0