The equations of the diagonals of the square formed by the pairs of straight lines $3 x^{2} + 8 x y - 3 y^{2} = 0$ and $3 x^{2} + 8 x y - 3 y^{2} + 2 x - 4 y - 1 = 0$ are?

x = 2 y, 4 x + 2 y + 1 = 0

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2 x + y = 0, 2 x = 4 y + 1

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x = 2 y, 2 x = 4 y + 1

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2 x + y = 0, 4 x + 2 y + 1 = 0

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Solution

The correct option is B $2 x + y = 0, 2 x = 4 y + 1$
$\begin{matrix} Given pair of straight lines are \begin{matrix} 3 x^{2} + 8 x y - 3 y^{2} = 0 3 x^{2} + 8 x y - 3 y^{2} + 2 x - 4 y - 1 = 0 \end{matrix} - (2) Partial differentiate with respect to x \Rightarrow 6 x + 8 y + 2 = 0 - (3) Partial differentiate with respect to y \Rightarrow 8 x - 6 y - 4 = 0 - (4) \end{matrix}$

$\begin{matrix} To find point of intersection of (3) and (4) x = \frac{5}{25} = \frac{1}{25}; y = - \frac{2}{5} To find equation of diagonals slope of A C = \frac{- 2 / 5 - 0}{1 / 5 - 0} = - 2 Slope of D B = y = - 2 x = \frac{1}{2} \end{matrix}$
$\begin{matrix} Equation of BD: y + \frac{1}{5} = \frac{1}{2} (x - \frac{1}{10}) \Rightarrow 10 x - 20 y = 5 \Rightarrow 2 x - 4 y = 1 Equation of A C which is 1 to B C \Rightarrow - 4 x + 2 y = k (- \frac{1}{5}, \frac{1}{10}) \Rightarrow \frac{4}{5} + \frac{1}{5} = k \Rightarrow k = 1 A C : 2 x + y = 0 then, (B) is the correct option. \end{matrix}$

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Q. Equation of straight line midway between the lines

x + 2 y - 1 = 0

and

2 x + 4 y - 5 = 0

Q. The equations of the tangents drawn from the point (0, 1) to the circle

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

are

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x y + 3 y^{2} - x + 4 y - 7 = 0

2 x y + y^{2} - 2 x - 2 y + 1 = 0

Q. Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

(i)

x + y = 5, 2 x + 2 y = 10

(ii)

x - y = 8, 3 x - 3 y = 16

(iii)

2 x + y - 6 = 0, 4 x - 2 y - 4 = 0

(iv)

2 x - 2 y - 2 = 0, 4 x - 4 y - 5 = 0

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The equations of the diagonals of the square formed by the pairs of straight lines 3x2+8xy−3y2=0 and 3x2+8xy−3y2+2x−4y−1=0 are?

The equations of the diagonals of the square formed by the pairs of straight lines $3 x^{2} + 8 x y - 3 y^{2} = 0$ and $3 x^{2} + 8 x y - 3 y^{2} + 2 x - 4 y - 1 = 0$ are?