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