Question

Let PQ be a chord of the parabola \(y^{2}=12 x\) and the midpoint of PQ be at \((4,1)\). Then, which of the following point lies on the line passing through the points P and Q?

(1) \((3,-3)\)

(2) \(\left(\frac{3}{2},-16\right)\)

(3) \((2,-9)\)

(4) \(\left(\frac{1}{2},-20\right)\)

Answer 1

Correct option is (4) \(\left(\frac{1}{2},-20\right)\)

\(\mathrm{T}=\mathrm{S}_{1}\)

\(\mathrm{y}-6(\mathrm{x}+4)\)

\(=1-48\)

\(6 x-y=23\)

Option 4, \(\left(\frac{1}{2},-20\right)\) will satisfy.