Coordinate Geometry
Hyperbola
MMTS_Full_Test_09
Grade 12
Question:
Which is/are true: I) A variable circle cuts two fixed perpendicular lines so that each intercept is of different length, then locus of centre is hyperbola. II) For hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ with focal chord at eccentric angles $\theta_1,\theta_2$: $e=\frac{\cos((\theta_1+\theta_2)/2)}{\cos((\theta_1-\theta_2)/2)}=\frac{\sin(\theta_1+\theta_2)}{\sin\theta_1+\sin\theta_2}$.
Only S-I is true
Only S-II is true
Both S-I and S-II are True
Both S-I and S-II are false
Step-by-Step Solution
Key Concept: Statement I about locus being hyperbola; Statement II is a known formula for hyperbola
S-I: True (locus is indeed a rectangular hyperbola). S-II: True (standard formula). Both true.
Correct Answer: 3