A variable point `P` is on the circle `x^2 + y^2 =1` on xy plane. From point P, perpendicular PN is drawn to the line `x =y =z` then the minimum length of PN is:-

A point P is taken on the circle x^(2)+y^(2)=a^(2) and PN, PM are draw, perpendicular to the axes. The locus of the pole of the line MN is

A point P is taken on the circle x^(2)+y^(2)=a^(2) and PN, PM are draw, perpendicular to the axes. The locus of the pole of the line MN is

Let P be a point on the circle x^(2)+y^(2)=9 , Q a point on the line 7x+y+3=0 , and the perpendicular bisector of PQ be the line x-y+1=0 . Then the coordinates of P are

A point P on the parabola y^2=12x . A foot of perpendicular from point P is drawn to the axis of parabola is point N. A line passing through mid-point of PN is drawn parallel to the axis interescts the parabola at point Q. The y intercept of the line NQ is 4. Then-

A point P on the parabola y^2=12x . A foot of perpendicular from point P is drawn to the axis of parabola is point N. A line passing through mid-point of PN is drawn parallel to the axis interescts the parabola at point Q. The y intercept of the line NQ is 4. Then-

The coordinates of the foot of the perpendicular drawn from the point P(x,y,z) upon the zx- plane are-

Let P be a variable point on the parabola y = 4x ^(2) +1. Then, the locus of the mid- point of the point P and the foot of the perpendicular drawn from the point P to the line y =x is:

The product of the perpendiculars drawn from the point (1,2) to the pair of lines x^(2)+4xy+y^(2)=0 is