Wah How to use "Have got to"

We know that have to is used for expressing a strong obligation or to give an idea of deduction when we are sure something is true from some evidence in this topic Wah How to use "Must and Have to"

Have got to has the same meaning as have to.
Have got to is used in British English much more than in American English.

Even though have got to has the present perfect form. In fact it is a present tense.

Affirmative    
    I have got to lose weight
    We have got to pay all our bills today.
    Maria has got to work so hard this week.

Negative
    I haven't got to lose weight
    We haven't got to pay all our bills today.
    Maria hasn't got to work so hard this week.

Interrogative
    Have I  got to lose weight?
    Have we got to pay all our bills today?
    Has Maria got to work so hard this week?

Have got to compared with Have to
    I don't have to finish reading this book today.
    I haven't got to finish reading this book today.

    Do you have to finish reading this book today? 
    Yes, I do.
    No, I don't.

    Have you got to finish reading this book today? 
    Yes, I have.
    No, I haven't.

The abbreviated forms of  've or 's are only used with have got - not with have.
    I have got to buy a toothpaste. = I've got to buy a toothpaste.
    but  I've to buy a toothpaste. is incorrect.

Sometime have got to may be abbreviated in informal speech.
    I have got to be back home by eight o'clock. = I got to be back home by eight o'clock.
    John has got to wait for you = John got to wait for you.

I've got to see the doctor.