Chord with a Given Mid Point : Ellipse

Q. Equation of the chord of the hyperbola $25x^2-16y^2=400$ which is bisected at the point (6, 2), is

1. 16x – 75y = 418
2. 75x - 16y = 418
3. 25x - 4y = 400
4. None of these

Q. Three distinct chords drawn from $(\alpha ,0)$ to the ellipse $x^2+2y^2=1.$ If these chords are bisected by the parabola $y^2=4x,$ then $\left[\alpha \right]=$
(where $[.]$ denotes greatest integer function)

Q.

What is the equation of chord of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ whose middle point is $(x_1,y_1)$ ? You are given. $T=\frac{x{x}_1}{a^2}+\frac{y{y}_1}{b^2}-1and{S}_1\frac{x_1^2}{a^2}+\frac{y_1^2}{b^2}-1$

1. $T+S_1=0$

2. $T=S_1$

3. $T+S_1=1$

4. $T+1=S_1$