Q58 / 110 · VITEEE 2023 · Mathematics

The equation of the tangent to the parabola \(y^2=6 x\) at the point whose ordinate is 6 , is

  • A
    \(x+2 y+6=0\)
  • B
    \(2 x-y+6=0\)
  • Correct answer
    C
    \(x-2 y+6=0\)
  • D
    \(x-y+6=0\)

Solution

Let \(x_1\) be the abscissa of the point whose ordinate is 6 . Since the point \(\left(\mathrm{x}_1, 6\right)\) lies on \(\mathrm{y}^2=6 \mathrm{x}\), \(\therefore 36=6 \mathrm{x}_1 \text { or } \mathrm{x}_1=6\) \(\therefore\) The point is \((6,6)\) Equation of tangent at \((6,6)\) is \(\begin{aligned} & \mathrm{y} \cdot 6=2 \cdot \frac{3}{2}(\mathrm{x}+6) \quad\left(\because \mathrm{yy}_1=2 \mathrm{a}\left(\mathrm{x}+\mathrm{x}_1\right)\right) \\ & \text { or } \mathrm{x}-2 \mathrm{y}+6=0 \end{aligned}\)

Hence, the correct answer is option: 'C'.

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