Let the lines `(y-2)=m_1(x-5)` and `(y+4)=m_2(x-3)` intersect at right angles at `P` (where `m_1a n dm_2` are parameters). If the locus of `P` is `x^2+y^2gx+fy+7=0` , then the value of `|f+g|` is__________

Let the lines (y-2)=m_(1)(x-5) and (y+4)=m_(2)(x-3) intersect at right angles at P (where m_(1) and m_(2) are parameters). If locus of P is x^(2)+y^(2)+gx+fy+7=0 , then ((g)/(2))^(2)+((f)/(2))^(2)-7 is equal to

Let O be the origin and P be a variable point on the circle x^(2)+y^(2)+2x+2y=0 .If the locus of mid-point of OP is x^(2)+y^(2)+2gx+2fy=0 then the value of (g+f) is equal to -

y-1=m_(1)(x-3) and y-3=m_(2)(x-1) are two family of straight lines,at right angled to each other The locus of their point of intersection is

If the angle between the two lines represented by 2x^(2)+5xy+3y^(2)+6x+7y+4=0 is tan^(-1)(m), then find the value of m.

If the co-ordinates of a point P are x = at^(2) , y = a sqrt(1 - t^(4)) , where t is a parameter , then the locus of P is a/an

If the circles x ^(2) + y ^(2) + 5x -6y-1=0 and x ^(2) + y^(2) +ax -y +1=0 intersect orthogonally (the tangents at the point of intersection of the circles are at right angles), the value of a is

Let P be a point on the hyperbola x^(2)-y^(2)=a^(2), where a is a parameter,such that P is nearest to the line y=2x. Find the locus of P.

The lines x+y-1=0,(m-1)x+(m^(2)-7)y-5=0 and (m-2)x+(2m-5)y=0 are concurrent for three values of m concurrent for no value of m parallel for one value of m parallel for two value of m

If m is the minimum value of f(x,y)=x^(2)-4x+y^(2)+6y when x and y are subjected to the restrictions 0<=x<=1 and 0<=y<=1, then the value of |m| is