Question

The line x + y = 2 cuts the ellipse 3x² + 2y² = 6 in A and B. Then the mid point of AB is

• A. (1, 1)
• B. $\left( \frac{4}{5},\frac{6}{5} \right)$
• C. $\left( \frac{6}{5},\frac{4}{5} \right)$
• D. $\left( \frac{2}{5},\frac{3}{5} \right)$

Answer 1

Answer: (B)

$\left( \frac{4}{5},\frac{6}{5} \right)$

Answer 2

The mid point of the chord of $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ on the line lx+my+n = 0 is

$\left( \frac{\mathbf{-}\mathbf{a}^{\mathbf{2}}\mathcal{l}\mathbf{n}}{\mathbf{a}^{\mathbf{2}}\mathcal{l}^{\mathbf{2}}\mathbf{+}\mathbf{b}^{\mathbf{2}}\mathbf{m}^{\mathbf{2}}}\mathbf{,}\mathbf{\mspace{6mu}}\frac{\mathbf{-}\mathbf{b}^{\mathbf{2}}\mathbf{mn}}{\mathbf{a}^{\mathbf{2}}\mathcal{l}^{\mathbf{2}}\mathbf{+}\mathbf{b}^{\mathbf{2}}\mathbf{m}^{\mathbf{2}}} \right)$=

$\left( \frac{\mathbf{-}\mathbf{2x1x}\mathbf{-}\mathbf{2}}{\mathbf{2x1 + 3x1}}\mathbf{,}\mathbf{\mspace{6mu}}\frac{\mathbf{-}\mathbf{3x1x}\mathbf{-}\mathbf{2}}{\mathbf{2x1 + 3x1}} \right)$ = (4/5, 6/5)