Let ( x , y ) ∈ ( R × R ) and a → = x i ^ + 2 j ^ - k ^ , b → = 6 i ^ - y j ^ + 2 k ^ be two vectors. If | a → × b → | 2 + | a → . b → | 2 = f ( x ) g ( y ) then f ( x ) + g ( y ) - 46 = 0 represents

Question

Let ( x , y ) ∈ ( R × R ) and a → = x i ^ + 2 j ^ - k ^ , b → = 6 i ^ - y j ^ + 2 k ^ be two vectors. If | a → × b → | 2 + | a → . b → | 2 = f ( x ) g ( y ) then f ( x ) + g ( y ) - 46 = 0 represents, a pair of lines, an ellipse, a hyperbola, a circle

MARKS App · Accepted Answer

a → × b → 2 + a → · b → 2 = a → 2 b → 2 - a → · b → 2 + a → · b → 2 = a → 2 b → 2 = x 2 + 4 + 1 2 36 + y 2 + 4 2 = f x g y ⇒ f x = x 2 + 5 , g y = y 2 + 40 Now, f x + g y - 46 = 0 ⇒ x 2 + y 2 = 1 ⇒ x - 0 2 + y - 0 2 = 1 , represents a circle with centre 0 , 0 & radius 1 units.

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