Equation of the line which is perpendicular to $9 x - 5 y + 6 = 0$ and passing through $(- 6, 6)$ is

9 x - 5 y + 9 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5 x + 9 y - 24 = 0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

5 x + 9 y = 24

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5 x + 9 y + 13 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $5 x + 9 y - 24 = 0$
Given,a line $^{'} 1^{'}$
$1 : 9 x - 5 y + 6 = 0 \Rightarrow 5 y = 9 x + 6 \Rightarrow y = \frac{9}{5} x + \frac{6}{5}$
Slope of the above line is $m_{1} = \frac{9}{5}$
Let the slope of the line perpendicular to the above line be $m_{2}$ .Then using the condition for perpendicularity we can write.
$m_{1} . m_{2} = - 1 \Rightarrow \frac{9}{5} . m_{2} = - 1 \Rightarrow m_{2} = \frac{- 5}{9}$
$∴$ The equation of the line slope $\frac{- 5}{9}$ and passing through $(- 6, 6)$ will be given by
$(y - 6) = \frac{- 5}{9} (x + 6) \Rightarrow 9 y - 54 = - 5 x - 30 \Rightarrow 5 x + 9 y - 24 = 0$ .

Suggest Corrections

Similar questions

(3, 4)

5 x + 9 y + 12 = 0

Equation of a straight line passing through the point $(4, 5)$ and equally inclined to the lines $3 x = 4 y + 7$ and $5 y = 12 x + 6$ is

The equation of the line passing through $(1, 5)$ and perpendicular to the line $3 x - 5 y + 7 = 0$ is

3 x + 5 y = 19

(3, 2)

Join BYJU'S Learning Program