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Distinguishing between Conics from General Equation and Eccentricity

The square of...

Question

The square of distance between the point of intersection of the lines represented by the equation $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$ and origin, is

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None of these

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Solution

The correct option is A

$S t a n d a r d R e s u l t$

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Similar questions

a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0

\frac{c (a + b) - f^{2} - g^{2}}{a b - h^{2}}

a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0

(\frac{b g - h f}{h^{2} - a b}, \frac{a f - g h}{h^{2} - a b})

a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0

(\sqrt{(\frac{f^{2} - b c}{h^{2} - a b})}, \sqrt{(\frac{g^{2} - a c}{h^{2} - a b})})

a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0

\sqrt{\frac{g^{2} - a c}{f^{2} - b c}} =

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0

b g^{2} = a f^{2}

h^{2} = a b

2 \sqrt{\frac{g^{2} - a c}{a (a + b)}}

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