The equation of the tangent to the parabola \(y^2=16 x\), which is perpendicular to the line \(3 x-4 y+5=0\)…

The equation of the tangent to the parabola \(y^2=16 x\), which is perpendicular to the line \(3 x-4 y+5=0\) is given by
  1. \(4 x-3 y+9=0\)
  2. \(4 x+3 y-9=0\)
  3. \(4 x+3 y+9=0\)
  4. \(4 x-3 y-9=0\)

Solution

Equation of tangent to the parabola \(y^2=16 x\) which is perpendicular to the line \(3 x-4 y+5=0\). So, slope of tangent is \(\left(-\frac{4}{3}\right)\) Therefore equation of tangent is \(\begin{aligned} & y=-\frac{4}{3} x+\frac{4}{-4 / 3} \Rightarrow y=-\frac{4}{3} x-3 \\ \Rightarrow \quad 4 x+3 y+9 & =0. \end{aligned}\)

Asked in: AP EAMCET 2020 (18 Sep Shift 1)

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