Statement I: A variable circle cuts two fixed perpendicular lines so that each intercept is of different length, then locus of the centre of the circle is hyperbola.

Question

Which of the following is/are true

Statement I: A variable circle cuts two fixed perpendicular lines so that each intercept is of different length, then locus of the centre of the circle is hyperbola.

Statement II: If the eccentric angles of the extremities of a focal chord of a Hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ are $θ_{1}$ and $θ_{2}$ , then eccentricity of the Hyperbola $e = \frac{\cos (\frac{θ_{1} + θ_{2}}{2})}{\cos (\frac{θ_{1} - θ_{2}}{2})} = \frac{\sin (θ_{1} + θ_{2})}{\sin θ_{1} + \sin θ_{2}}$

Smart Achievers · Accepted Answer

(3)

Refer to properties of conics

Solution

1 Only Statement I is true

2 Only Statement II is true

3 Both Statement I and II are True

4 Both Statement I and II are false

Ans.
(3)

Refer to properties of conics

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