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 & y = \(9x\over 4\) + 1

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