HyperbolaHardBloom L3
Question
A circle cuts two perpendicular lines so that each intercept has given length. The locus of the centre of the circle is a conic whose eccentricity is:
Options
A.1
B.$\frac{1}{\sqrt{2}}$
C.$\sqrt{2}$
D.none of these
Solution
Sol. (c) $r^{2} = \frac{l_{1}^{2}}{4} + k^{2} = \frac{l_{2}^{2}}{4} + h^{2}$
$$\Rightarrow \ x^{2} - y^{2} = \frac{l_{1}^{2} - l_{2}^{2}}{4}$$
Which is rectangular hyperbola
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