TS EAMCET · Maths · Parabola
For the parabola \(y=\frac{h^3}{3} x^2+\frac{h^2}{2} x-h+\frac{3}{4 h^3}\) if the equation of directrix is \(y=k\), then \(k: h\)
- A \(16: 19\)
- B \(-19: 16\)
- C \(20: 27\)
- D \(-27: 20\)
Answer & Solution
Correct Answer
(B) \(-19: 16\)
Step-by-step Solution
Detailed explanation
Given, \(\quad y=\frac{h^3}{3} x^2+\frac{h^2}{2} x-h+\frac{3}{4 h^3}\) \(12 h^3 y=4 h^6 x^2+6 h^5 x-12 h^4+9\) \(4 h^6 x^2+6 h^5 x=12 h^3 y+12 h^4-9\) \(\left(x^2+\frac{3}{2 h} x\right)=\frac{12 h^4}{4 h^6}\left(y+\frac{12 h^4}{12 h^3}-\frac{3}{14 h^3}\right)\)…
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