Question

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

• A. 4x + 25y = 29
• B. 5x +25y = 30
• C. 25x + 4y = 29
• D. 25x + 5y = 30

Answer 1

The correct option is A

4x + 25y = 29

Equation of chord of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ whose middle point is $(x_1,y_1)$ is given by $T=S_1$ or

$\frac{x{x}_1}{a^2}+\frac{y{y}_1}{b^2}-1=\frac{x_1^2}{a^2}+\frac{y_1^2}{b^2}-1$

The given ellipse is $4x^2+25y^2=100$ or

$\frac{x^2}{25}+\frac{y^2}{4}=1$ and the point is (1,1)

$T=S_1\Rightarrow \frac{1x}{25}+\frac{1y}{4}-1=\frac{1}{25}+\frac{1}{4}-1$

$\Rightarrow 4x+25y=4+25$

=29

4x+25y =29