Math Assignment Help With Point Of Contact Of A line And A Parabola

7.5.8 Point of contact of a line and a parabola:

The point of contact of a line y = mx + (a/m) with parabola y2 = 4ax is given by;

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Example: Find the equation of the tangent to the parabola y2 = 9x, passing through (4, 10). Find its point of contact.

Solution; equation of parabola: y2 = 9x

a = 9/4

let the equation of tangent be

y = mx + a/m

y = mx + 9/4m

as it passes through (4, 10),

10 = 4m + 9/4m

16m2 – 40m + 9 = 0

(4m – 1)(4m – 9) = 0

Therefore,

m = 1/4 or m = 9/4

putting the values of m, the required equation of tangents are;

x – 4y + 36 = 0

9x – 4y + 4 = 0

Putting the values of m in

point of contact of a line and a parabola

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