If `(x_r, y_r) ; r= 1, 2, 3, 4` be the points of intersection of the parabola `y^2 = 4ax` and the circle `x^2 + y^2+ 2gx +2fy +c=0`, then

Let (x_r,y_r),r =1,2,3,4 ne the points of intersection the parabola "y^2=4ax" and the circle"x^2+y^2+2gx+2fy+c=0"prove that y_1+y_2+y_3+y_4=0

If the origin lies inside the circle x^(2) + y^(2) + 2gx + 2fy + c = 0 , then

If the circle x ^(2) + y^(2) + 2gx + 2fy+ c=0 touches X-axis, then

The equation of the normal at P(x_(1),y_(1)) to the circle x^(2)+y^(2)+2gx+2fy+c=0 is

Let A(x_(1), y_(1))" and "B(x_(2), y_(2)) be two points on the parabola y^(2)=4ax . If the circle with chord AB as a diameter touches the parabola, then |y_(1)-y_(2)|=

Tangent to the parabola y=x^(2)+ax+1 at the point of intersection of the y-axis also touches the circle x^(2)+y^(2)=r^(2) . Also, no point of the parabola is below the x-axis. The minimum area bounded by the tangent and the coordinate axes is

Tangent to the parabola y=x^(2)+ax+1 at the point of intersection of the y-axis also touches the circle x^(2)+y^(2)=r^(2) . Also, no point of the parabola is below the x-axis. The radius of circle when a attains its maximum value is