The equation of the pair of straight lines passing through the point $(2,3)$ and perpendicular to the pair of lines $3x^2-4xy+5y^2=0$ is $ax^2+2hxy+by^2+2gx+2fy+c=0$. Then $a+b+c+f+g+h=$

The three sides of a triangle are given by $(x^2+7xy+2y^2)(y-1)=0$. Then the centroid of that triangle is

The equation of the pair of straight lines perpendicular to the pair $ax^2 + 2hxy + by^2 = 0$ is

If the sum of slopes of the pair of lines given by $4x^{2} + 2hxy - 7y^{2} = 0$ is equal to the product of the slopes,then $h$ is

If angles made by lines $x^2 - 4xy - y^2 = 0$ with the positive direction of the $x$-axis are $\theta_1$ and $\theta_2$,then the value of $\sec^2(\theta_1 + \theta_2) + |\frac{1}{\tan \theta_1} + \frac{1}{\tan \theta_2}|$ is

If $x^2-y^2+2hxy+2gx+2fy+c=0$ is the locus of a point which moves such that it is always equidistant from the lines $x+2y+7=0$ and $2x-y+8=0$,then the value of $g+c+h-f$ equals