Question

The equation(s) of tangents to the parabola $y^2$ = 12x, which passes through the point (2,5) is/are:

• A. y = x + 3
• B. y = x - 3
• C. 2y = 3x - 4
• D. 2y = 3x + 4

Answer 1

Answer: (A), (D)

2y = 3x + 4

We know that the equation of a tangent to $y^2$=4ax having slope m is given by-
$y=\mathrm{mx}+\frac{a}{m}\mathrm{As}a=3\Rightarrow y=\mathrm{mx}+\frac{3}{m}\mathrm{As}\mathrm{this}\mathrm{tangent}\mathrm{passes}\mathrm{through}\mathrm{the}\mathrm{point}(2,5)5=2m+\frac{3}{m}\mathrm{or}2m^2-5m+3=0\mathrm{or}m=1,\frac{3}{2}\mathrm{On}\mathrm{putting}\mathrm{the}\mathrm{value}\mathrm{of}m,\mathrm{the}\mathrm{equation}\mathrm{of}\mathrm{the}\mathrm{tangents}\mathrm{are}:y=x+3\mathrm{and}2y=3x+4$