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8. An ellipse confocal with the hyperbola and with eccentricity equal to 1/(sqrt(2)) is intersected by the line x + y - 7 = 0 at A and B, then intersection point of tangents at A and B will lie on
A) x + y - 8 = 0
B) x + y - 9 = 0
C) x + y - 11 = 0
D) x + y - 13 = 0?
Most Upvoted Answer
8. An ellipse confocal with the hyperbola and with eccentricity equal ...
Given Information:
- Ellipse is confocal with the hyperbola.
- Eccentricity of the ellipse is 1/√2.
- Line x + y - 7 = 0 intersects the ellipse at points A and B.

Solution:

Confocal Ellipse and Hyperbola:
- The ellipse and hyperbola are confocal if they share the same foci.
- Given that the eccentricity of the ellipse is 1/√2, which means its center is at the origin.

Line Intersection with Ellipse:
- The line x + y - 7 = 0 intersects the ellipse at points A and B.
- Let the equation of the ellipse be x^2/a^2 + y^2/b^2 = 1.
- Substituting the equation of the line in the ellipse equation, we get x^2/a^2 + (7-x)^2/b^2 = 1.
- Since the line intersects the ellipse at two points, we can solve for a^2 and b^2.

Intersection Point of Tangents:
- The intersection point of tangents at A and B lies on the line joining the points A and B.
- The equation of the line passing through A and B is x + y = 7.
- Therefore, the intersection point of tangents lies on the line x + y - 7 = 0.

Conclusion:
- The intersection point of tangents at A and B will lie on the line x + y - 7 = 0.
- So, the correct option is A) x + y - 8 = 0.
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8. An ellipse confocal with the hyperbola and with eccentricity equal to 1/(sqrt(2)) is intersected by the line x + y - 7 = 0 at A and B, then intersection point of tangents at A and B will lie onA) x + y - 8 = 0B) x + y - 9 = 0C) x + y - 11 = 0D) x + y - 13 = 0?
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8. An ellipse confocal with the hyperbola and with eccentricity equal to 1/(sqrt(2)) is intersected by the line x + y - 7 = 0 at A and B, then intersection point of tangents at A and B will lie onA) x + y - 8 = 0B) x + y - 9 = 0C) x + y - 11 = 0D) x + y - 13 = 0? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 8. An ellipse confocal with the hyperbola and with eccentricity equal to 1/(sqrt(2)) is intersected by the line x + y - 7 = 0 at A and B, then intersection point of tangents at A and B will lie onA) x + y - 8 = 0B) x + y - 9 = 0C) x + y - 11 = 0D) x + y - 13 = 0? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 8. An ellipse confocal with the hyperbola and with eccentricity equal to 1/(sqrt(2)) is intersected by the line x + y - 7 = 0 at A and B, then intersection point of tangents at A and B will lie onA) x + y - 8 = 0B) x + y - 9 = 0C) x + y - 11 = 0D) x + y - 13 = 0?.
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