The radius of the circle 𝐶 is ___ .
Correct Answer: 1.5
Solution and Explanation
Let the circle be,
(x – a)2 + y2 = r2
Solving it with parabola
y2 = 4 – x we get
(x – a)2 + 4 – x = r2
x2 – x(2a + 1) + (a2 + 4 – r2) = 0 …(1)
D = 0
\(⇒\) 4r2 + 4a – 15 = 0
Clearly a ≥ r
So 4r2 + 4r – 15 ≤ 0
\(⇒\) rmax =\(\frac{3}{2}\) = a
Radius of circle C is \(\frac{3}{2}\)
The value of 𝛼 is ___ .
Correct Answer: 2
Solution and Explanation
Let the circle be,
(x – a)2 + y2 = r2
Solving it with parabola
y2 = 4 – x we get
(x – a)2 + 4 – x = r2
x2 – x(2a + 1) + (a2 + 4 – r2) = 0 …(1)
D = 0
\(⇒\) 4r2 + 4a – 15 = 0
Clearly a ≥ r
So 4r2 + 4r – 15 ≤ 0
\(⇒\) rmax = \(\frac{3}{2}\) = a
Radius of circle C is \(\frac{3}{2}\)
From (1) x2 – 4x + 4 = 0
\(⇒ x = 2 = α\)
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