Question

The locus of mid points of the chords of the ellipse $2x^2+3y^2=4$ each of which makes an angle ${45}^o$ with the x- axis is:

• A. $3x+4y=0$
• B. $4x+3y=0$
• C. $3x+2y=0$
• D. $2x+3y=0$

Answer 1

The correct option is D $2x+3y=0$

The equation of chord with mid point $(x_1,y_1)is$

$\frac{x{x}_1}{a^2}+\frac{y{y}_1}{b^2}=\frac{x{{}_1}^2}{a^2}+\frac{y{{}_1}^2}{b^2}$

$2x{x}_1+3y{y}_1=2x{{}_1}^2+3y{{}_1}^2$

But given slope $=1$

$\Rightarrow \frac{-2x_1}{3y_1}=1\Rightarrow 3y_1+2x_1=0$

$\therefore$ locus is $3y+2x=0$