JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let a common tangent to the curves \(y^2=4 x\) and \((x-4)^2+y^2=16\) touch the curves at the points \(P\) and \(Q\). Then \(( PQ )^2\) is equal to \(..........\).
- A \(31\)
- B \(30\)
- C \(33\)
- D \(32\)
Answer & Solution
Correct Answer
(D) \(32\)
Step-by-step Solution
Detailed explanation
General tangent of slope \(m\) to the circle \((x-4)^2+\) \(y ^2=16\) is given by \(y=m(x-4) \pm 4 \sqrt{1+m^2}\) General tangent of slope \(m\) to the parabola \(y^2=4 x\) is given by \(y=m x+\frac{1}{m}\) For common tangent \(\frac{1}{m}=-4 m \pm 4 \sqrt{1+m^2}\)…
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