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

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none of these

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Solution

The correct option is A $3 x^{2} - 4 x y + 5 y^{2} = 0$
Here the mirror image of line $3 x^{2} + 4 x y + 5 y^{2} = 0$ in mirror $x = 0$
i.e about $Y - a x i s$
So the x-coordinates About $Y - a x i s$ becomes negative and the y-coordiantes remains same Hence putting $x = - x$ in given eq
$3 (- x)^{2} - 4 (- x) y + 5 y^{2} = 0$
$3 x^{2} - 4 x y + 5 y^{2} = 0$

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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

by 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

Question 82 (ii)

Subtract

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

Question 82 (ii)

Subtract

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

Q. If

8 - 3 (x + 2) = - 10

and

7 (2 y - 3) = 3 + 8 y;

find the value of

: 3 x^{2} - 4 x y - 5 y^{2} .

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

The correct option is A 3x2−4xy+5y2=0Here the mirror image of line 3x2+4xy+5y2=0 in mirror x=0i.e about Y−axisSo the x-coordinates About Y−axis becomes negative and the y-coordiantes remains same Hence putting x=−x in given eq 3(−x)2−4(−x)y+5y2=03x2−4xy+5y2=0

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