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Question
The conic section represented by the equation 2xy+4x-6y+17=0 is
The conic section represented by the equation 2xy+4x-6y+17=0 is
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Solution
The correct option is D Hyperbola
On comparing the given equation with standard 2nd degree equation i.e. ax2+by2+2hxy+2gx+2fy+c=0, we get:
a = 0, b = 0, c = 17, g = 2, f = -3, h = 1
∴Δ=abc+2fgh−af2−bg2−ch2=−12−17=−29≠0and h2−ab=1−0>0
H e n c e , t h e g i v e n e q u a t i o n r e p r e s e n t s
a h y p e r b o l a .
On comparing the given equation with standard 2nd degree equation i.e. ax2+by2+2hxy+2gx+2fy+c=0, we get:
a = 0, b = 0, c = 17, g = 2, f = -3, h = 1
∴Δ=abc+2fgh−af2−bg2−ch2=−12−17=−29≠0and h2−ab=1−0>0