AP EAMCET · Maths · Parabola
A common tangent to the circle \(x^2+y^2=9\) and parabola \(y^2=8 x\) is
- A \(3 x-\sqrt{3} y+2=0\)
- B \(x-\sqrt{3} y+6=0\)
- C \(2 x-\sqrt{3} y+3=0\)
- D \(x-3 y+6=0\)
Answer & Solution
Correct Answer
(B) \(x-\sqrt{3} y+6=0\)
Step-by-step Solution
Detailed explanation
Let \(y=m x+c\) be the equation of common tangent to parabola \(y^2=8 x\) and \(x^2+y^2=9\) Condition for \(y=m x+c\) to be the tangent of \(y^2=4 a x\) is \(c=\frac{a}{m}\) So, \(c=\frac{2}{m}\) ....(i) The line \(y=m x+c\) is tangent to circle \(x^2+y^2=9\)…
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