JEE MATHEMATICS MCQ: PAIR OF STRAIGHT LINES

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Analyzing +4 | -1

If the system of equations

a x+h y+g=0, h x+b y+f=0

and

a x^{2}+2 h x y+b y^{2}+2 g x+2 f y+c+t

=0

has a unique solution, then

View answer and explanation

Correct option: C

t=\frac{a b c+2 f g h-a f^{2}-b g^{2}-c h^{2}}{h^{2}-a b}

Option C is correct because after rationalizing and simplifying the limit, the expression converges to 1/(4√2) as y approaches infinity.

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