TS EAMCET · Maths · Ellipse
The midpoint of the chord of the ellipse \(x^2+\frac{y^2}{4}=1\) formed on the line \(y=x+1\) is
- A \(\left(\frac{4}{5}, \frac{9}{5}\right)\)
- B \(\left(-\frac{1}{5}, \frac{4}{5}\right)\)
- C \(\left(\frac{1}{5}, \frac{6}{5}\right)\)
- D \(\left(-\frac{6}{5},-\frac{1}{5}\right)\)
Answer & Solution
Correct Answer
(B) \(\left(-\frac{1}{5}, \frac{4}{5}\right)\)
Step-by-step Solution
Detailed explanation
Equation of chord with midpoint \( (x_1, y_1) \): \( x x_1 + \frac{y y_1}{4} = x_1^2 + \frac{y_1^2}{4} \) Comparing with given line \( y=x+1 \Rightarrow x-y+1=0 \): \( \frac{x_1}{1} = \frac{y_1/4}{-1} = \lambda \) \( x_1=\lambda, y_1=-4\lambda \) Midpoint \( (x_1, y_1) \) lies…
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