The image of the pair of lines represented by $3 x^{2} + 4 x y + 5 y^{2} = 0$ by the line mirror $x = 0$ is

3 x^{2} - 4 x y + 5 y^{2} = 0

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3 x^{2} - 4 x y - 5 y^{2} = 0

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5 x^{2} - 4 x y - 3 y^{2} = 0

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none of these

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Solution

The correct option is A $3 x^{2} - 4 x y + 5 y^{2} = 0$
Replacing $x$ by $- x$ , the image of the pair of lines $3 x^{2} + 4 x y + 5 y^{2} = 0$ is
$3 x^{2} + 4 y (- x) + 5 y^{2} = 0 \Rightarrow 3 x^{2} - 4 x y + 5 y^{2} = 0$

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Similar questions

Q. The image of the pair of lines represented by

3 x^{2} + 4 x y + 5 y^{2} = 0

in the line mirror

x = 0

If the bisector of the angles of the lines represented by $3 x^{2} - 4 x y + 5 y^{2} = 0$ and $5 x^{2} + 4 x y + 3 y^{2} = 0$ are same, then the angle made by the lines represented by first with the second, is

Q. The angle between the pair of straight lines

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

Q. Find the separate equation of the lines represented by the following equation:
(i)

3 y^{2} + 7 x y = 0

(ii)

5 x^{2} - 9 y^{2} = 0

(iii)

x^{2} - 4 x y = 0

(iv)

3 x^{2} - 10 x y - 8 y^{2} = 0

Question 82 (ii)

Subtract

$6 x^{2} - 4 x y + 5 y^{2} f r o m 8 y^{2} + 6 x y - 3 x^{2}$

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The image of the pair of lines represented by 3x2+4xy+5y2=0 by the line mirror x=0 is

The correct option is A 3x2−4xy+5y2=0Replacing x by −x, the image of the pair of lines 3x2+4xy+5y2=0 is3x2+4y(−x)+5y2=0⇒3x2−4xy+5y2=0

The image of the pair of lines represented by $3 x^{2} + 4 x y + 5 y^{2} = 0$ by the line mirror $x = 0$ is

The correct option is A $3 x^{2} - 4 x y + 5 y^{2} = 0$
Replacing $x$ by $- x$ , the image of the pair of lines $3 x^{2} + 4 x y + 5 y^{2} = 0$ is
$3 x^{2} + 4 y (- x) + 5 y^{2} = 0 \Rightarrow 3 x^{2} - 4 x y + 5 y^{2} = 0$