# Find the equation of the tangents to the parabola $$y^2$$ = 9x which go through the point (4,10).

## Solution :

Equation of tangent to the parabola $$y^2$$ = 9x is

y = mx + $$9\over 4m$$

Since it passes through (4,10)

$$\therefore$$  10 = 4m + $$9\over 4m$$ $$\implies$$ 16$$m^2$$ – 40m + 9 = 0

m = $$1\over 4$$, $$9\over 4$$

$$\therefore$$ Equation of tangent’s are y = $$x\over 4$$ + 9 &amp; y = $$9x\over 4$$ + 1

### 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).

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

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