The distance of the point of intersection of the lines 2x – 3y + 5 = 0 and 3x + 4y = 0 from the line 5x – 2y = 0 is

Given two lines are:

2x – 3y + 5 = 0 …(i)

and 3x + 4y = 0 …(ii)

Now, point of intersection of these lines can be find out as:

Multiplying eq. (i) by 3, we get

6x – 9y + 15 = 0 …(iii)

Multiplying eq. (ii) by 2, we get

6x + 8y = 0 …(iv)

On subtracting eq. (iv) from (iii), we get

6x – 9y + 15 – 6x – 8y = 0

⇒ – 17y + 15 = 0

⇒ - 17y = -15

On putting value of y in eq. (ii), we get

So, the point of intersection of given two lines is:

Now, perpendicular distance from the point to the given line 5x – 2y = 0

Hence, the correct option is (a)