If (h,k) is a point on the axis of the parabola `2(x-1)^2 + 2(y-1)^2 = (x+y+2)^2 `from where three distinct normal can be drawn, then the least integral value of h is :

The set of points on the axis of the parabola (x-1)^2=8(y+2) from where three distinct normals can be drawn to the parabola is the set (h ,k) of points satisfying (a)h >2 (b) h >1 (c)k >2 (d) none of these

From a point (sintheta,costheta) , if three normals can be drawn to the parabola y^(2)=4ax then the value of a is

If the circle (x-6)^(2)+y^(2)=r^(2) and the parabola y^(2)=4x have maximum number of common chords, then the least integral value of r is __________ .

Three normals with slopes m_1, m_2 and m_3 are down from a point P not on the axis of the axis of the parabola y^2 = 4x . If m_1 m_2 = alpha , results in the locus of P being a part of parabola, Find the value of alpha

If there exists at least one point on the circle x^(2)+y^(2)=a^(2) from which two perpendicular tangents can be drawn to parabola y^(2)=2x , then find the values of a.

Column I, Column II Points from which perpendicular tangents can be drawn to the parabola y^2=4x , p. (-1,2) Points from which only one normal can be drawn to the parabola y^2=4x , q. (3, 2) Point at which chord x-y-1=0 of the parabola y^2=4x is bisected., r. (-1,-5) Points from which tangents cannot be drawn to the parabola y^2=4x , s. (5,-2)

Find the number of distinct normals that can be drawn from (-2,1) to the parabola y^2-4x-2y-3=0

Find the equation of tangents drawn to the parabola y=x^2-3x+2 from the point (1,-1)dot

The area of the region bounded by the parabola (y-2)^(2) = x- 1 , the tangent to the parabola at the point (2,3) and the x-axis is

If x + y = k is a normal to the parabola y^(2) = 12x then the value of k is