Question

If two distinct chords drawn from the point (4, 4) on the parabola y² = 4ax are bisected on the line y = mx, then the set of value of m is given by-

• A. $\left( \frac { 1 - \sqrt { 2 } } { 2 } , \frac { 1 + \sqrt { 2 } } { 2 } \right)$
• B. R
• C. (0, )
• D. (–2, 2)

Answer 1

Answer: (A)

$\left( \frac { 1 - \sqrt { 2 } } { 2 } , \frac { 1 + \sqrt { 2 } } { 2 } \right)$

Answer 2

Any point on the line y = mx can be taken as (t, mt). Equation of the chord of parabola with this as mid point y m t – 2 (x + t) = m² t² – 4t It passes through (4, 4)

4mt – 2(4 + t) = m² t² – 4t

Ž m²t² – 2 (2m + 1) t + 8 = 0 we want two such chords

D > 0 (2m + 1)² – 8 m² > 0

4m² – 4m – 1 < 0 Ž $\frac { 1 - \sqrt { 2 } } { 2 }$< m < $\frac { 1 + \sqrt { 2 } } { 2 }$