AP EAMCET · Maths · Parabola
The equation of one of the common tangents of the circle \(x^2+y^2-6 y+4=0\) and the parabola \(y^2=x\) is
- A \(2 x-y+1=0\)
- B \(2 x-y=1\)
- C \(4 x-y+1=0\)
- D \(x-2 y+1=0\)
Answer & Solution
Correct Answer
(D) \(x-2 y+1=0\)
Step-by-step Solution
Detailed explanation
Let the equation of tangent to the parabola \(y^2=x\), having slope \(m\) is, \[ y=m x+\frac{1}{4 m} \] For common tangent to the circle \[ x^2+y^2-6 y+4=0 \] \(\therefore\) Radius \(\sqrt{9-4}=\frac{\left|3-\frac{1}{4 m}\right|}{\sqrt{1+m^2}}\)…
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