Question

In which region the curve y²(a + x) = x²(3a – x) does not lie? 

(a) x > 0 

(b) 0 < x < 3a 

(c) x ≤ – a and x > 3a 

(d) – a < x < 3a 

Answer 1

(c) x ≤ – a and x > 3a

y²(a + x) = x²(3a – x) 

Taking y = 0 (1) ⇒ 0 = x² (3a – x) 

= x = 0, x = 3a 

∴ The points are (0, 0) (3a, 0) 

There is a loop between x = 0 and x = 3a

When x > 3 a, y ➝ imaginary 

The curves does not exist beyond x = 3a i.e., x > 3a 

The curve has asymptote at x = -a 

The curve does not exist when x < -a 

The curve exists in the region – a < x < 3a