Find the equations of two perpendicular straight lines, both pass thru the point 3x+4y-7=0, 5x-12y+7 = 0 and 1 passes thru the point (2,9)?

I am going to interpret this differently, in order to get two equations, which the original question asks for:
"Find the equations of the two straight lines, perpendicular to 3x+4y-7=0 and 5x-12y+7=0 respectively, and both passing through the point (2,9)."

Now, the line perpendicular to ax+by+c=0 through a given point (x₀,y₀) is bx-ay-(bx₀-ay₀)=0.

So, the equation of the straight line, perpendicular to 3x+4y-7=0 and passing through the point (2,9) is 4x-3y-(4×2-3×9)=0 which simplifies to 4x-3y+19=0 ← Linear equation ①
And, the equation of the straight line, perpendicular to 5x-12y+7=0 and passing through the point (2,9) is -12x-5y-(-12×2-5×9)=0 which simplifies to 12x+5y-69=0 ← Linear equation ②

Perpendicular Straight Lines

assume you meant " the intersection point of "
[ y - 1 ] = 8 [ x - 1 ] and [ y - 2 ] = ( - 1 / 8 ) [ x - 2 ]