If b = a + cp and r = ab + (frac{1}{2})cp

^{2}, express b^{2}in terms of a, c, r.-
**A.**

b^{2}= aV + 2cr -
**B.**

b^{2}= ar + 2c^{2}r -
**C.**

b^{2}= a^{2}= (frac{1}{2}) cr^{2} -
**D.**

b^{2}= (frac{1}{2})ar^{2}+ c -
**E.**

b^{2}= 2cr – a^{2}

##### Correct Answer: Option E

##### Explanation

b = a + cp….(i)

r = ab + (frac{1}{2})cp^{2}…..(ii)

expressing b^{2} in terms of a, c, r, we shall first eliminate p which should not appear in our answer from eqn, (i)

b – a = cp = (frac{b – a}{c})

sub. for p in eqn.(ii)

r = ab + (frac{1}{2})c(frac{(b – a)^2}{frac{ab + b^2 – 2ab + a^2}{2c}})

2cr = 2ab + b^{2} – 2ab + a^{2}

b^{2} = 2cr – a^{2}