Let A(3, 0) and B(4, 1) are two points on the parabola `y=(x-3)^(2)`, find a point on this parabola where its tangent is parallel to the chord AB.

Let A(4,-4) and B(9,6) be points on the parabola y^(2)=4x. Let C be chosen on the on the arc AOB of the parabola where O is the origin such that the area of DeltaACB is maximum. Then the area (in sq. units) of DeltaACB is :

Find the point on the parabola y^2=2x which is closest to the point (1,4).

Find the point on the parabla y=x^(2)-6x+9 , where the tangent is paralle to the line joining the points (4,1) and (3,0).

Let A and B be two distinct points on the parabola y^2=4x . If the axis of the parabola touches a circle of radius r having AB as its diameter, then find the slope of the line joining A and B .

Let A, B be two distinct points on the parabola y^(2)=4x . If the axis of the parabola touches a circle of radius r having AB as diameter, the slope of the line AB is

Let A(x_(1),y_(1)) and B(x_(2),y_(2)) be two points on the parabola y^(2) = 4ax . If the circle with chord AB as a dimater touches the parabola, then |y_(1)-y_(2)| is equal to

Prove that the chord y-xsqrt(2)+4asqrt(2)=0 is a normal chord of the parabola y^2=4a x . Also find the point on the parabola when the given chord is normal to the parabola.

The mirror image of the parabola y^2= 4x in the tangent to the parabola at the point (1, 2) is:

Find the where the tangents to the parabola y=x^(2) is paralle to the line y=4x-5

Find a point on the curve y = (x – 2)^(2) at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).