Consider a parabola `S: x^2=-4(y-4)` and a line L:y=x+8.S intersects x-axis at A and B and L intersects x-axis at C such that C, A and B are collinear in order. If a point P is chosen on 'L' such that tangents drawn from it to 'S' are perpendicular, then to

Consider a parabola S:x^2= -4 (y -4) and a line L:y= x+8. 'S' intersects x-axis at A and B and L intersects x-axis at C such that C, A and B are collinear in order. f a point Pv is chosen on L such that angle APB is maximum and P is not collinear with A and B, then find PC and PB

Consider with circle S:x^(2)+y^(2)-4x-1=0 and the line L:y=3x-1 .If the line L cuts the circle at A and B then Length of the chord AB equal

The line 4x-7y+10=0 intersects the parabola,y^(2)=4x at the points A&B .The co- ordinates of the point of intersection of the tangents drawn at the points A&B are:

A normal is drawn to parabola y^2=4x at (1,2) and tangent is drawn to y=e^x at (c,e^c) . If tangent and normal intersect at x-axis then find C.

The parabola y=4-x^(2) has vertex P. It intersects x-axis at A and B. If the parabola is translated from its initial position to a new position by moving its vertex along the line y=x+4 , so that it intersects x-axis at B and C, then abscissa of C will be :

The sraight line 3x-4y+c=0 Intersects the parabola x^(2)=4y at the points A and B Ifthe tangents to the parabola at A and B are perpendicular,then c=

Consider a hyperbola xy = 4 and a line y = 2x = 4 . O is the centre of hyperbola. Tangent at any point P of hyperbola intersect the coordinate axes at A and B. Let the given line intersects the x-axis at R. if a line through R. intersect the hyperbolas at S and T, then minimum value of RS xx RT is