TS EAMCET · Maths · Parabola
If the normal drawn at \(\mathrm{P}(8,16)\) to the parabola \(y^2=32 x\) meets the parabola again at Q, then the equation of the tangent drawn at Q to the parabola is
- A \(x+3 y+72=0\)
- B \(x-y-120=0\)
- C \(3 x-y-264=0\)
- D \(x+y-24=0\)
Answer & Solution
Correct Answer
(A) \(x+3 y+72=0\)
Step-by-step Solution
Detailed explanation
\(y^2=32x \implies 4a=32 \implies a=8\) For \(\mathrm{P}(8,16)\), \(2at_1=16 \implies 2(8)t_1=16 \implies t_1=1\) Normal at \(t_1\) meets parabola at \(t_2\): \(t_2 = -t_1 - \frac{2}{t_1}\) \(t_2 = -1 - \frac{2}{1} = -3\) Coordinates of \(\mathrm{Q}\):…
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