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The equation of tangent of parabola y2 = 9x at point (4, 6) is:
1. 3x – 4y + 12 = 0
2. 3y – 4x + 12 = 0
3. 3x – 4y = 12
4. 3y – 4x = 12
5. None of these

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Correct Answer - Option 1 : 3x – 4y + 12 = 0

Concept:

The equation of tangent of parabola

y2 = 4ax at the point (x1, y1) is given by: yy1 = 2a (x + x1)

Calculation:

Given:

Equation of parabola is y2 = 9x

Let point P = (4, 6)

Here, a = \(\frac94\), x1 = 4 and y1 = 6.

As we know that, the equation of tangent of parabola y2 = 4ax at the point (x1, y1) is given by: yy1 = 2a (x + x1).

⇒ 6y = \(\frac{9(x + 4)}2\)

⇒ 12y = 9x + 36

⇒ 3x – 4y + 12 = 0

Hence, the equation of required tangent is: 3x – 4y + 12 = 0

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