Prove that the length of any chord of the parabola `y^(2) = 4 ax` passing through the vertex and making an angle `theta ` with the positive direction of the x-axic is `4a cosec theta cot theta `

Length of the focal chord of the parabola y^2=4ax at a distance p from the vertex is:

Length of the shortest normal chord of the parabola y^2=4ax is

Show that the locus of the middle points of chords of the parabola y^(2) = 4ax passing through the vertex is the parabola y^(2) = 2ax

Show that the locus of the middle points of chords of the parabola y^(2) = 4ax passing through the vertex is the parabola y^(2)= 2ax .

If the equation of the pair of straight lines passing through the point (1,1) , one making an angle theta with the positive direction of the x-axis and the other making the same angle with the positive direction of the y-axis, is x^2-(a+2)x y+y^2+a(x+y-1)=0,a!=2, then the value of sin2theta is

The locus of the midpoints of all chords of the parabola y^(2) = 4ax through its vertex is another parabola with directrix is

If the length of a focal chord of the parabola y^2=4a x at a distance b from the vertex is c , then prove that b^2c=4a^3 .

A normal chord of the parabola y^2=4ax subtends a right angle at the vertex, find the slope of chord.

A tangent is drawn to parabola y^2=8x which makes angle theta with positive direction of x-axis. The equation of tangent is

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.