From a variable point p on line `2x−y-1=0` pair of tangents are drawn to parabola `x^2=8y` then chord of contact passes through a fixed point.

If the line x+y =1 is a tangent to the parabola y^(2)-y +x=0 , then the point of contact is-

y=x is tangent to the parabola y=ax^(2)+c . If c=2, then the point of contact is

From a point on the circle x^2+y^2=a^2 , two tangents are drawn to the circle x^2+y^2=b^2(a > b) . If the chord of contact touches a variable circle passing through origin, show that the locus of the center of the variable circle is always a parabola.

Tangents are drawn to x^2+y^2=1 from any arbitrary point P on the line 2x+y-4=0 . The corresponding chord of contact passes through a fixed point whose coordinates are (a) (1/2,1/2) (b) (1/2,1) (c) (1/2,1/4) (d) (1,1/2)

Tangent is drawn at any point (x_1, y_1) other than the vertex on the parabola y^2=4a x . If tangents are drawn from any point on this tangent to the circle x^2+y^2=a^2 such that all the chords of contact pass through a fixed point (x_2,y_2), then

Tangents are drawn from the points on the line x−y−5=0 to x^2+4y^2=4 , then all the chords of contact pass through a fixed point, whose coordinate are

Find the equation of the tangent to the parabola 9x^2+12 x+18 y-14=0 which passes through the point (0, 1).

Find the equation of tangents of the parabola y^2=12 x , which passes through the point (2, 5).

Tangent is drawn at any point (p ,q) on the parabola y^2=4a xdot Tangents are drawn from any point on this tangant to the circle x^2+y^2=a^2 , such that the chords of contact pass through a fixed point (r , s) . Then p ,q ,r and s can hold the relation (a) r^2q=4p^2s (b) r q^2=4p s^2 (c) r q^2=-4p s^2 (d) r^2q=-4p^2s

From a variable point on the tangent at the vertex of a parabola y^2=4a x , a perpendicular is drawn to its chord of contact. Show that these variable perpendicular lines pass through a fixed point on the axis of the parabola.