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

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 tangent to the parabola y= x^(2) + 6 at the point (1, 7) also touches the circle x^(2) + y^(2) + 16x + 12y + c =0 , then the coordinates of the point of contact are-

The tangent to the circle x^(2)+y^(2)=5 at (1, -2) also touches the circle x^(2)+y^(2)-8x+6y+20=0. Find the coordinates of the corresponding point of contact.

The tangent to the circle x^(2)+y^(2)=5 at the point (1, -2) also touches the circle x^(2)+y^(2)-8x+6y+20=0 at the point

If tangent to the parabola y^2=8x at (2,-4) also touches the circle x^2+y^2=a . then find the value of a

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

The tangent at the point P(x_1, y_1) to the parabola y^2 = 4 a x meets the parabola y^2 = 4 a (x + b) at Q and R. the coordinates of the mid-point of QR are