in the given figure `y=x^(2)+bx+c` is a quadratic polynomial which meets x-axis at A and B and y-axis at C Q is vertex of quadratic polynomial and foot of perpendicular from Q to x-axis and y-axis are P and R respectively. Then answer the following questions.
Q. if two circles passing through A and B touches y-axis at C and R respectively then

Options

A. `b^(2)=2c`
B. `b^(2)=3c`
C. `b^(2)=4c`
D. `b^(2)=8c`

Answer

C

Explanation

`OA.OB=OC^(2)`
`alpha.beta=c^(2)` & `((b^(2)-4c)/(4))^(2)=alphabeta`
`(b^(2)-4)^(2)=16`
`c=c^(2)` `b^(2)-4=4`
`c=1` `b^(2)=8`