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 normals can be drawn, then prove that `h > 2.`

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

The set of points on the axis of the parabola y^2=4x+8 from which the three normals to the parabola are all real and different is (a) {(k ,0)"|"klt=-2} (b) {(k ,0)"|"kgt=-2} (c) {(0, k)"|"k gt=-2} (d) none of these

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 point where the line x+y=6 is a normal to the parabola y^2=8xdot

IF three distinct normals to the parabola y^(2)-2y=4x-9 meet at point (h,k), then prove that hgt4 .

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

Statement 1: If there exist points on the circle x^2+y^2=a^2 from which two perpendicular tangents can be drawn to the parabola y^2=2x , then ageq1/2 Statement 2: Perpendicular tangents to the parabola meet at the directrix.

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

If three distinct normals can be drawn to the parabola y^2-2y=4x-9 from the point (2a ,b) , then find the range of the value of adot