JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let A be the point \((3, 0)\) and circles with variable diameter AB touch the circle \(x^2 + y^2 = 36\) internally. Let the curve C be the locus of the point B. If the eccentricity of C is \(e\), then \(72e^2\) is equal to _______.
- A 6
- B 9
- C 18
- D 36
Answer & Solution
Correct Answer
(C) 18
Step-by-step Solution
Detailed explanation
Let the coordinates of point B be \((h, k)\). The center of the circle with diameter AB is \(C_1 \left( \dfrac{h+3}{2}, \dfrac{k}{2} \right)\) and its radius is \(r_1 = \dfrac{1}{2} \sqrt{(h-3)^2 + k^2}\). The given circle is \(x^2 + y^2 = 36\), which has center \(C_2(0, 0)\)…
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