PQ is a chord of the parabola `y^(2) = 4ax ` . The ordinate of P is twice that of Q . Prove that the locus of the mid - point of PQ is `5y^(2) = 18 ax `

PN is any ordinate of the parabola y^(2) = 4ax , the point M divides PN in the ratio m: n . Find the locus of M .

Q is any point on the parabola y^(2) =4ax ,QN is the ordinate of Q and P is the mid-point of QN ,. Prove that the locus of p is a parabola whose latus rectum is one -fourth that of the given parabola.

PQ is any focal chord of the parabola y^(2)=8 x. Then the length of PQ can never be less than _________ .

A point on the parabola y^(2)=18x at which the ordinate increases at twice the rate of the abscissa is-

P,Q and R three points on the parabola y^(2)=4ax . If Pq passes through the focus and PR is perpendicular to the axis of the parabola, show that the locus of the mid point of QR is y^(2)=2a(x+a) .

Find the area bounded by the parabola y^(2) =4ax and its double ordinate x =b

Two tangents to the parabola y^(2)=4ax meet at an angle alpha . Prove that the locus of their of intersections, is y^(2)-4ax=(x+a)^(2) tan^(2) alpha

let P be the point (1, 0) and Q be a point on the locus y^2= 8x . The locus of the midpoint of PQ is

Let P be the point (1,0) and Q be a point on the locus y^(2)=8x . The locus of the midpoint of PQ is

PQ is a double ordinate of the parabola y^2=4ax Show that thelocus of its point of trisection the chord PQ is 9y^2=4ax .