#### Given : A circle,   and a parabola, Statement - I : An equation of a common tangent to these curves is Statement - II : If the line , is their common tangent, then m satisfies . Option 1) Statement - I is false ; Statement - II is true.   Option 2) Statement - I is ture ; Statement - II is true ; Statement - II is a correct explanation for statement - I.     Option 3) Statement - I is ture ; Statement - II is true ; Statement - II is not a correct explanation for statement - I.     Option 4) Statement - I is ture ; Statement - II is false.

As we learnt in

Condition of tangency -

- wherein

If    is a tangent to the circle

and

Equation of tangent -

- wherein

Tengent to is slope form.

Tangent to circle is

Tangent to parabola is

So,

On solving m=1

Thus tangent is

Option 1)

Statement - I is false ; Statement - II is true.

This option is incorrect.

Option 2)

Statement - I is ture ; Statement - II is true ; Statement - II is a correct explanation for statement - I.

This option is incorrect.

Option 3)

Statement - I is ture ; Statement - II is true ; Statement - II is not a correct explanation for statement - I.

This option is correct.

Option 4)

Statement - I is ture ; Statement - II is false.

This option is incorrect.