AP EAMCET · Maths · Parabola
The equation of the common tangent to the parabolas \(y^2=32 x\) and \(x^2=256 y\) is
- A \(x+2 y-32=0\)
- B \(x+2 y+32=0\)
- C \(2 x+y-32=0\)
- D \(2 x+y+32=0\)
Answer & Solution
Correct Answer
(B) \(x+2 y+32=0\)
Step-by-step Solution
Detailed explanation
Tangent to \(y^2=32x\) (\(a=8\)): \(y=mx+\frac{8}{m}\) Tangent to \(x^2=256y\) (\(b=64\)): \(y=mx-64m^2\) For common tangent: \(\frac{8}{m}=-64m^2\) \(m^3 = -\frac{8}{64} = -\frac{1}{8}\) \(m=-\frac{1}{2}\) Substitute \(m\) into tangent equation:…
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