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Every Point on the Bisector of an Angle Is Equidistant from the Sides of the Angle.

For the pair ...

Question

For the pair of straight lines given by the equation $3 x^{2} - 5 x y + 2 y^{2} - 11 x + 9 y + 10 = 0$ which of the following condition holds?

f^{2} = b c

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a b c = 2 f g h

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b g^{2} \neq c h^{2}

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2 f g h = b g^{2} + c h^{2}

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Solution

The correct option is D $2 f g h = b g^{2} + c h^{2}$
$3 x^{2} - 5 x y + 2 y^{2} - 11 x + 9 y + 10 = 0$
Compare with
$a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$
$a = 3, h = \frac{- 5}{2}, b = 2, g = \frac{- 11}{2}, f = \frac{9}{2}, c = 10$
correct option is D.

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Similar questions

If the equation
$a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$
represents a pair of straight lines, then
$a b c + 2 f g h - a f^{2} - b g^{2} + c h^{2} = 0$

If the pair of lines $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$ intersect on the y axis, then

Q. Assertion :If the equation

6 x^{2} - 42 x y + 60 y^{2} - 11 x + 10 y + λ = 0

represents two straight lines, then

λ = 10.

Reason: The second degree equation

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

represents a pair of straight lines if

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

If the equation
$a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$
represents a pair of straight lines, then
$a b c + 2 f g h - a f^{2} - b g^{2} + c h^{2} = 0$

Q. Assertion :The equation

3 x^{2} - 2 y^{2} + 4 x - 6 y = 0

represents a hyperbola. Reason: The second degree equation

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

represents a hyperbola if

a b c + 2 f g h - a f^{2} - b g^{2} - c h^{2} \neq 0

h^{2} > a b

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For the pair of straight lines given by the equation 3x2−5xy+2y2−11x+9y+10=0 which of the following condition holds?

The correct option is D 2fgh=bg2+ch23x2−5xy+2y2−11x+9y+10=0Compare withax2+2hxy+by2+2gx+2fy+c=0a=3,h=−52,b=2,g=−112,f=92,c=10correct option is D.

For the pair of straight lines given by the equation $3 x^{2} - 5 x y + 2 y^{2} - 11 x + 9 y + 10 = 0$ which of the following condition holds?

The correct option is D $2 f g h = b g^{2} + c h^{2}$
$3 x^{2} - 5 x y + 2 y^{2} - 11 x + 9 y + 10 = 0$
Compare with
$a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$
$a = 3, h = \frac{- 5}{2}, b = 2, g = \frac{- 11}{2}, f = \frac{9}{2}, c = 10$
correct option is D.