Question

Show that the curves 6x² – 5x + 2y = 0, 4x² + 8y² = 3 touch each other at (1/2, 1/2). 

Answer 1

Given curve equations are 

6x² – 5x + 2y = 0 –––––––– (1) 

4x² + 8y² = 3 –––––––– (2) 

Differentiating (1) w.r.to 'x' on both sides

12x - 5 + 2dy/dx = 0

differentiating (2) w.r.to 'x' on both sides

= –1/2 

∴ m₁ = m₂ 

∴ Given curves (1) & (2) touch each other at (1/2, 1/2)