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The line y = m*x meets the ellipse 2x² + y² = 1 at a point P in the first quadrant. The normal to the ellipse at P cuts the coordinate axes at (-1/(3*sqrt(2)), 0) and (0, beta). Find beta.
- 2/sqrt(3)
- 2*sqrt(2)/3
- 2/3
- sqrt(2)/3
Correct answer: 2*sqrt(2)/3
Solution
The x-intercept condition fixes P, and substituting into the y-intercept of the normal gives beta = 2*sqrt(2)/3.
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