A right-angled triangle `A B C` is inscribed in parabola `y^2=4x ,` where `A` is the vertex of the parabola and `/_B A C=pi/2dot` If `A B=sqrt(5),` then find the area of ` A B Cdot`

The vertex of the parabola y^2 + 4x = 0 is

An equilateral triangle is inscribed in the parabola y^(2) = 4ax whose vertex is at the vertex of the parabola. Find the length of its side.

An equilateral triangle is inscribed in the parabola y^(2)=4ax , where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

If chord BC subtends right angle at the vertex A of the parabola y^(2)=4x with AB=sqrt(5) then find the area of triangle ABC.

The triangle PQR of area 'A' is inscribed in the parabola y^2=4ax such that the vertex P lies at the vertex pf the parabola and base QR is a focal chord.The modulus of the difference of the ordinates of the points Q and R is :

The vertices A ,Ba n dC of a variable right triangle lie on a parabola y^2=4xdot If the vertex B containing the right angle always remains at the point (1, 2), then find the locus of the centroid of triangle A B Cdot

In a triangle A B C ,/_A=60^0a n db : e=(sqrt(3)+1):2, then find the value of (/_B-/_C)dot

A is a point on the parabola y^2=4a x . The normal at A cuts the parabola again at point Bdot If A B subtends a right angle at the vertex of the parabola, find the slope of A Bdot

An equilateral triangle S A B is inscribed in the parabola y^2=4a x having its focus at Sdot If chord A B lies towards the left of S , then the side length of this triangle is (a) 2a(2-sqrt(3)) (b) 4a(2-sqrt(3)) (c) a(2-sqrt(3)) (d) 8a(2-sqrt(3))

Find the locus of the middle points of the chords of the parabola y^2=4a x which subtend a right angle at the vertex of the parabola.