Find the equation to the straight line passing through the point $(2, - 9)$ and the intersection of the lines $2 x + 5 y - 8 = 0$ and $3 x - 4 y = 35$ .

Open in App

Solution

$3 x - 4 y = 35........ (i) 2 x + 5 y = 8 \Rightarrow x = \frac{8 - 5 y}{2}$

substituting $x$ in $(i)$

$3 (\frac{8 - 5 y}{2}) - 4 y = 35 24 - 15 y - 8 y = 70 - 23 y = 46 \Rightarrow y = - 2 x = \frac{8 - 5 (- 2)}{2} \Rightarrow x = 9$

So the point of intersection is $P (9, - 2)$

Equation of line joining $(2, - 9)$ and $P$ is

$y - (- 2) = (\frac{- 9 - (- 2)}{2 - 9}) (x - 9) y + 2 = \frac{- 7}{- 7} (x - 9) y + 2 = x - 9 x - y = 11$

Suggest Corrections

Similar questions

Q. Find the equation of the line joining the point

(2, - 9)

and the point of intersection of lines

2 x + 5 y - 8 = 0

and

3 x - 4 y - 35 = 0.

The equation of the straight line passing through the point of intersection of lines 3x – 4y – 7 = 0 and 12x – 5y – 13 = 0 and perpendicular to the line 2x – 3y + 5 = 0 is

Q. Find the equation of a straight line passing through the intersection of 2x+5y-4=0 with X axis and perpendicular to the line 3x-7y+8=0

Q. Find the equations to the straight lines that pass through the intersection of the lines

2 x - 3 y = 0

and

4 x - 5 y = 2

and

(i)

Passes through the point

(2, 1)

(i i)

Is perpendicular to the line

x + 2 y + 1 = 0

(i i i)

Is parallel to the line

3 x - 4 y + 5 = 0

Q. Find the equation of a straight line passing through the point of intersection of x + 2y + 3 = 0 and 3x + 4y + 7 = 0 and perpendicular to the straight line x − y + 9 =0

Join BYJU'S Learning Program

Find the equation to the straight line passing through the point (2,−9) and the intersection of the lines 2x+5y−8=0 and 3x−4y=35.

3x−4y=35........(i)2x+5y=8⇒x=8−5y2 substituting x in (i) 3(8−5y2)−4y=3524−15y−8y=70−23y=46⇒y=−2x=8−5(−2)2⇒x=9 So the point of intersection is P(9,−2) Equation of line joining (2,−9) and P is y−(−2)=(−9−(−2)2−9)(x−9)y+2=−7−7(x−9)y+2=x−9x−y=11

Find the equation to the straight line passing through the point $(2, - 9)$ and the intersection of the lines $2 x + 5 y - 8 = 0$ and $3 x - 4 y = 35$ .