The correct option (a) 9x – 7y = 1
Explanation:
Line is equally inclined to lines 3x – 4y – 7 = 0 and 12x – 5y + 6 = 0
∴ [(3x – 4y – 7)/√(32 + 42)] = ± [(12x – 5y + 6)/√{122 + 52}]
∴ [(3x – 4y – 7)/5] = ± [(12x – 5y + 6)/(13)]
i.e. 21x + 27y + 121 = 0
99x – 77y – 61 = 0
i.e. their slopes are [(– 7)/9] and (9/7)
∴ equation of line with slope [(– 7)/9] and through point (4, 5) is
y – 5 = [(– 7)/9](x – 4) ⇒ 7x + 9y = 73
equation of line with slope (9/7) and through point (4, 5) is
y – 5 = (9/7)(x – 4) ⇒ 9x – 7y = 1
