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

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 slope of the tangents when the radius of the circle is maximum 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 slope of the tangents when the radius of the circle is maximum 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 minimum area bounded by the tangent and the coordinate axes is (a) 1 (b) 1/3 (c) 1/2 (d) 1/4

If the circle x^(2)+y^(2)+2ax=0, a in R touches the parabola y^(2)=4x , them

Locus of point of intersection of perpendicular tangents to the circle x^(2)+y^(2)-4x-6y-1=0 is

The locus of the point of intersection of the perpendicular tangents to the circle x^(2)+y^(2)=a^(2), x^(2)+y^(2)=b" is "

The point of intersection of the tangent to the parabola y^(2)=4x which also touches x^(2)+y^(2)=(1)/(2) is

y=3x is tangent to the parabola 2y=ax^2+ab . If (2,6) is the point of contact , then the value of 2a is

The angle between tangents to the parabola y^(2)=4x at the points where it intersects with the line x-y -1 =0 is

If the normals of the parabola y^(2)=4x drawn at the end points of its latus rectum are tangents to the circle (x-3)^(2)+(y+2)^(2)=r^(2) , then the value of r^(4) is equal to