JEE Advanced Mathematics question

Mathematics Parabola JEE Advanced

is the equation of Column I: (i) a circle if is (ii) a parabola if is (iii) an ellipse if is (iv) a hyperbola if is Column II: (a) (b) (c) (d)

(1)(i)-(a), (ii)-(b), (iii)-(d), (iv)-(c)
(2)(i)-(d), (ii)-(c), (iii)-(a), (iv)-(b)
(3)(i)-(d), (ii)-(a), (iii)-(b), (iv)-(c)
(4)(i)-(d), (ii)-(b), (iii)-(a), (iv)-(c)Correct

Answer: (4)

Solution

Compare with ax^2+2hxy+by^2+2gx+2fy+c=0: , so

-ab=(λ--λ=λ^2-3λ+1 .

The conic is non-degenerate when \Delta=abc+2fgh-af^2-bg^2-ch^2\ne0. Here

Δ=λ+(λ-1)-λ-94-(λ-=

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Question ID VK-110271