The sum of the slopes of the tangent of the parabola \(y^2\)=4ax drawn from the point (2,3) is

Solution :

The equation of tangent to the parabola \(y^2\) = 4ax is y = mx + \(a\over m\).

Since it is drawn from point (2,3)

Therefore it lies on tangent y = mx + \(a\over m\).

\(\implies\) 3 = 2m + \(a\over m\)

\(\implies\) 3m = 2\(m^2\) + a

\(\implies\)  2\(m^2\) – 3m + a = 0

Now, Sum of slopes is \(3\over 2\).       [  \(\because\) sum of roots = \(-b\over a\) ]


Similar Questions

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

Leave a Comment

Your email address will not be published.