﻿ The lines 2x + 3y + 4 = 0 and 3x – 2y + 5 = 0 may be conjugate w.r.t. the hyperbola  if : Kaysons Education

# The Lines 2x + 3y + 4 = 0 And 3x – 2y + 5 = 0 May Be Conjugate W.r.t. The Hyperbola  if

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## Question

### Solution

Correct option is

2x + 3y + 4 = 0               ….. (1),

3x – 2y + 5 = 0                …. (2)

Are conjugate lines w.r.t. hyperbola

…. (3)

Let (x1y1) be pole of line (1) w.r.t. (3). Then its polar is

…. (4)

Compare (1) and (4),

.

By assumption (1) and (2) are conjugate, so pole of line (1) lies on (2)

⇒ 3x1 – 2y+ 5 = 0

⇒ 3a2 + 3b2 = 10

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