Question
Find the equation of the conic of which one focus lies at (2, 1), one directrix x + y = 0 and it passes through (4,1) . Also identify the conic.
Answer :
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Skip in 10
To find the equation of the conic, we use the definition that a conic is the locus of a point whose distance from the focus is in a constant ratio (eccentricity \( e \)) to its distance from the directrix. ### Given Data: - Focus: \( F(2,1) \) - Directrix: \( x + y = 0 \) - Point on the conic: \( P(4,1) \) Let \( (x, y) \) be a general point on the conic. The distance of this point from the focus is: \[ \text{Distance from } F(2,1) = \sqrt{(x - 2)^2 + (y - 1)^2} \] The perpendicular distance of \(
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