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Question
Answer the following:
Find the equation of the tangent to the parabola y2 = 9x at the point (4, −6) on it
Solution
The equation of the tangent to the parabola y2 = 4ax at the point (x1, y1) is yy1 = 2a(x + x1)
The equation of the parabola is y2 = 9x
Comparing this equation with y2 = 4ax, we get,
∴ 4a = 9
∴ 2a = `9/2`
∴ the equation of the tangent to the given parabola at (4, – 6) is
y(– 6) = `9/2(x + 4)`
∴ – 2y = `3/2(x + 4)`
∴ – 4y = 3x + 12
∴ 3x + 4y + 12 = 0.
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