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AP EAMCET · Maths · Parabola

Equation of the line touching both parabolas \(y^2=4 x\) and \(x^2=-32 y\) is

  1. A \(x+2 y+4=0\)
  2. B \(2 x+y-4=0\)
  3. C \(x-2 y-4=0\)
  4. D \(x-2 y+4=0\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(x-2 y+4=0\)

Step-by-step Solution

Detailed explanation

\(y^2=4 x\) ...(i) Equation of tangent of (i) is, \(y=m x+\frac{1}{m}\), ...(ii) Also, \(x^2=-32 y\) ...(iii) Equation of tangent of (iii) is \(y=m x-(-8 m)^2 \Rightarrow y=m x+8 m^2\) ...(iv) From (ii) and (iv), \(\frac{1}{m}=8 m^2 \Rightarrow m=\frac{1}{2}\) So, from (ii),…