Let P(h,k) be the mid point of chord of the parabola \(y^2\) = 4ax,
so equation of chord is yk – 2a(x+h) = \(k^2\) – 4ah.
Since it passes through (p,q)
\(\therefore\) qk – 2a(p+h) = \(k^2\) – 4ah
\(\therefore\) Required locus is \(y^2\) – 2ax – qy + 2ap = 0
The slope of the line touching both the parabolas \(y^2\) = 4x and \(x^2\) = -32 is
What is the equation of tangent to the parabola having slope m?
Find the equation of the tangents to the parabola \(y^2\) = 9x which go through the point (4,10).
Find the value of k for which the point (k-1, k) lies inside the parabola \(y^2\) = 4x.
The length of latus rectum of a parabola, whose focus is (2, 3) and directrix is the line x – 4y + 3 = 0 is