Chord with a Given Mid Point : Ellipse

Q. Chord of an ellipse are drawn through the positive end of the minor axis. Then their mid-point lies on

1. a circle
2. a parabola
3. an ellipse
4. a hyperbola

Q.

Find the equation of the chord of the ellipse $4x^2+25y^2=100$ whose middle point is (1, 1).

1. 4x +25y =29

2. 5x+25y=30

3. 25x +4y=29

4. 25x +5y =30

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. $T+1=S_1$

Q. The equation of the line, passing through the centre and bisecting the chord $7x+y-1=0$ of the ellipse $\frac{x^2}{1}+\frac{y^2}{7}=1,$ is

1. $x-7y=0$
2. $7x-y=0$
3. $x-y=0$
4. $x+y=0$

Q. The locus of mid-points of focal chords of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ with eccentricity $e$ is

1. $\frac{x^2}{a^2}+\frac{y^2}{b^2}=\frac{ex}{a}$
2. $\frac{x^2}{a^2}-\frac{y^2}{b^2}=\frac{ex}{a}$
3. $x^2+y^2=a^2+b^2$
4. None of the above