# 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 = $$-b\over a$$ ]

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