The equation of tangent in slope form to \(y^2\) = 4ax is
y = mx + \(a\over m\)
Now, if it is common to both parabola, it also lies on second parabola
then \(x^2\) = 4a(mx + \(a\over m\))
\(mx^2 – 4am^2 – 4a^2\) = 0 has equal roots.
then its discriminant is zero. i.e. \(b^2-4ac\) = 0
\(16a^2m^2 + 16a^2m\) = 0
m = -1
Putting m = -1 in equation y = mx + \(a\over m\) we get
y = -x – a
x + y + a = 0
Which is the required equation of common tangent to both parabola.
The slope of the line touching both the parabolas \(y^2\) = 4x and \(x^2\) = -32 is
Find the locus of middle point of the chord of the parabola \(y^2\) = 4ax which pass through a given (p, q).
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