What is the equation of the line which passes through $(4, - 5)$ and is perpendicular to $3 x + 4 y + 5 = 0$ ?

4 x - 3 y - 31 = 0

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

3 x - 4 y - 41 = 0

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

4 x + 3 y - 1 = 0

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

3 x + 4 y + 8 = 0

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

Open in App

Solution

The correct option is C $4 x - 3 y - 31 = 0$
Slope of the given line $3 x + 4 y + 5 = 0$ is $m_{1} = - \frac{3}{4}$
Slope of the line perpendicular to the given line is $\frac{- 1}{m_{1}} = \frac{- 1}{(\frac{- 3}{4})} = \frac{4}{3}$

The equation of the line which is perpendicular to $3 x + 4 y + 5 = 0$ and passing through point $(4, - 5)$ is $y - y_{1} = m (x - x_{1})$
$\Rightarrow y - (- 5) = \frac{4}{3} (x - 4) \Rightarrow 3 y + 15 = 4 x - 16 \Rightarrow 4 x - 3 y - 31 = 0$

Suggest Corrections

Similar questions

Find the equation of circle circumscribing the quadrilateral formed by four lines $3 x + 4 y - 5 = 0$ , $4 x - 3 y - 5 = 0$ , $3 x + 4 y + 5 = 0$ and $4 x - 3 y + 5 = 0$

Equations to the sides of a triangle are $x - 3 y = 0$ , $4 x + 3 y = 5$ and $3 x + y = 0$ . The line $3 x - 4 y = 0$ passes through the

Q. The equation of the sides of a triangle are

x - 3 y = 0, 4 x + 3 y = 5

and

3 x + y = 0

. The line

3 x - 4 y = 0

passes through:

Q. The equations of the tangents to the circle

x^{2} + y^{2} - 6 x + 4 y = 12

which are parallel to the straight line 4x + 3y + 5 = 0, are

Q. The equation of the straight line passing through the intersection of the lines

x - y - 1 = 0

and

2 x - 3 y + 1 = 0

and parallel to

3 x + 4 y - 14 = 0

Join BYJU'S Learning Program

What is the equation of the line which passes through (4,−5) and is perpendicular to 3x+4y+5=0?

What is the equation of the line which passes through $(4, - 5)$ and is perpendicular to $3 x + 4 y + 5 = 0$ ?