question_answer

If the line \[x+y=1\] is a tangent to a parabola with focus (1, 2) at A and intersects the directrix at B and tangent at vertex at C respectively, then \[AC\cdot BC\] is equal to

A) 2

B) 1

C) 1

D) 1

Correct Answer: A

Solution :

Using power of C \[BC\cdot AC=C{{S}^{2}}\] \[\therefore \] \[BC\cdot AC={{\left( \frac{1+2-1}{\sqrt{2}} \right)}^{2}}=2\]