Question

(α, β) lie on the parabola y² = 4x and (α, β) also lie on chord with mid-point \(\left(1,\frac {5}{4}\right)\) of another parabola x² = 8y, then value of |(8 – β)(α – 28)| is

(1) 192 

(2) 92 

(3) 64 

(4) 128

Answer 1

(1) 192 

Chord with point, T = S₁

(α, β) lie on (L1) and also y² = 4x

⇒ α − 4β + 4 = 0

β² = 4α

β² = 4(4β - 4)

β² − 16β + 16 = 0

\((28 +16 \sqrt {3},8+4\sqrt {3})\) and \((28 - 16 \sqrt {3},8-4\sqrt {3})\)

\((8-\beta)(\alpha - 28)\)

⇒ \((-4 \sqrt {3})(16 \sqrt {3})\)

= -192