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