The triangle formed by the lines $2x^2+xy-6y^2=0$ and $x+y-1=0$ is

The centroid of the triangle formed by the pair of straight lines $12x^2 - 20xy + 7y^2 = 0$ and the line $2x - 3y + 4 = 0$ is $(\alpha, \beta)$. Then,$\alpha + 2\beta =$

If $9x^2-24xy+16y^2+\alpha x+\beta y+6=0$ represents a pair of parallel lines $1$ unit apart and one of those lines passes through $(1,1)$,then $\frac{\alpha}{\beta} = $

If the area of the triangle formed by the pair of lines $8x^2-6xy+y^2=0$ and the line $2x+3y=a$ is $7$,then $a$ is equal to

The equations $x-y=4$ and $x^2+4xy+y^2=0$ represent the sides of a/an

Assertion $(A)$: The lines $2x^2 + 5xy + 2y^2 = 0$ and $x - 2y + 1 = 0$ form a right-angled triangle.
Reason $(R)$: The equation $ax^2 + 2hxy + by^2 = 0$ represents a pair of perpendicular lines if $a + b = 0$.
Choose the correct answer.