In demand curve the line does not touch the axis but in geometric method y does the curve or demand line touch the axis?????

When the demand curve intersects X-axis, it depicts perfectly inelastic demand and when it intersects Y-axis, it shows perfectly elastic demand. It should be noted that perfectly elastic or inelastic demand is an imaginary situation. That's why the demand curve does not touches the axes in real life situations.

However, under geometric method, we have to analyse all types of Elasticity of Demand. That's why demand curve intersects the axes under geometric method, so that we can come to know what perfectly elastic and perfectly inelastic demands are.