The line `y=x+asqrt2` touches the circle `x^2+y^2=a^2` at P. The coordinate of P are

The line y=x+a sqrt(2) touches the circle x^(2)+y^(2)=a^(2) at the point

If the line y=mx+asqrt(1+m^2) touches the circle x^2+y^2=a^2 , then the point of contact is

Line y=x+asqrt2 is a tangent to the circle x^2+y^2=a^2 at

The line y=6x+1 touches the parabola y^(2)=24x . The coordinates of a point P on this line, from which the tangent to y^(2) =24x is perpendicular to the line y=6x+1. is

The tangent to the parabola y=x^(2)-2x+8 at P(2, 8) touches the circle x^(2)+y^(2)+18x+14y+lambda=0 at Q. The coordinates of point Q are

The tangent to the parabola y=x^(2)-2x+8 at P(2, 8) touches the circle x^(2)+y^(2)+18x+14y+lambda=0 at Q. The coordinates of point Q are

A line parallel to the line x-3y=2 touches the circle x^(2)+y^(2)-4x+2y-5=0 at the point

Tangent to the curve y=x^(2)+6 at a point P(1, 7) touches the circle x^(2)+y^(2)+16x+12y+c=0 at a point Q. Then the coordinates of Q are

If the line px+qy=1 touches the circle x^(2)+y^(2)=r^(2), prove that the point (p,q) lies on the circle x^(2)+y^(2)=r^(-2)