JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
A line is a common tangent to the circle \((x-3)^{2}+y^{2}=9\) and the parabola \(y^{2}=4 x.\) If the two points of contact \(( a , b )\) and \(( c , d )\) are distinct and lie in the first quadrant, then \(2(a+c)\) is equal to ........ .
- A \(9\)
- B \(3\)
- C \(4\)
- D \(6\)
Answer & Solution
Correct Answer
(A) \(9\)
Step-by-step Solution
Detailed explanation
Let coordinate of point \(A \left( t ^{2}, 2 t \right) \quad(\because a =1)\) equation of tangent at point \(A\) \(y t=x+t^{2}\) centre of circle \((3,0)\) Now \(PD =\) radius \(\left|\frac{3-0+t^{2}}{\sqrt{1+t^{2}}}\right|=3\) \(\left(3+t^{2}\right)^{2}=9\left(1+t^{2}\right)\)…
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