Let a common tangent to the curves \( y^{2}=4x \) and \( (x-4)^{2}+y^{2}=16 \) touch the curves at the points \( P \) and \( Q \). Then \( (PQ)^{2} \) is equal to ________.
The combined equation of the two lines \( ax+by+c=0 \) and \( a'x+b'y+c'=0 \) can be written as \( (ax+by+c)(a'x+b'y+c')=0 \). The equation of the angle bisectors of the lines represented by the equation \( 2x^{2}+xy-3y^{2}=0 \) is:
Let the system of linear equations \( x+y+kz=2 \), \( 2x+3y-z=1 \), \( 3x+4y+2z=k \) have infinitely many solutions. Then the system\( (k+1)x+(2k-1)y=7 \)\( (2k+1)x+(k+5)y=10 \)has:
Let \( y=x+2 \), \( 4y=3x+6 \) and\( 3y=4x+1 \) be three tangent lines to the circle \( (x-h)^2+(y-k)^2=r^2 \). Then \( h+k \) is equal to:
