If `P(a sec alpha,b tan alpha)` and `Q(a secbeta, b tan beta)` are two points on the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` such that `alpha-beta=2theta` (a constant), then `PQ` touches the hyperbolaA. `(x^(2))/(a^(2)sec^(2)theta)-(y^(2))/(b^(2))=1`B. `(x^(2))/(a^(2))-(y^(2))/(b^(2)sec^(2)theta)=1`C. `(x^(2))/(a^(2))-(y^(2))/(b^(2))=cos^(2)theta`D. none of these

If `P(a sec alpha,b tan alpha)` and `Q(a secbeta, b tan beta)` are two

1.	If `P(a sec alpha,b tan alpha)` and `Q(a secbeta, b tan beta)` are two points on the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` such that `alpha-beta=2theta` (a constant), then `PQ` touches the hyperbolaA. `(x^(2))/(a^(2)sec^(2)theta)-(y^(2))/(b^(2))=1`B. `(x^(2))/(a^(2))-(y^(2))/(b^(2)sec^(2)theta)=1`C. `(x^(2))/(a^(2))-(y^(2))/(b^(2))=cos^(2)theta`D. none of these
Answer» The equation of chord `PQ` is `(x)/(a)cos((alpha-beta)/(2))-(y)/(b)sin((alpha+beta)/(2))=cos((alpha+beta)/(2))` `implies(x)/(a)costheta-(y)/(b)sin((alpha+beta)/(2))=cos((alpha+beta)/(2))` `implies(x)/(asectheta)sec((alpha+beta)/(2))-(y)/(b)tan((alpha+beta)/(2))=1` Clearly, it touches the hyperbola `(x^(2))/(a^(2)sec^(2)theta)-(y^(2))/(b^(2))=1`

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