1.

If the normal at a point P to the hyperbola meets the transverse axis at G, and the value of SG/SP is 6, then the eccentricity of the hyperbola is (where S is focus of the hyperbola)

Answer»

2
4
6
8

Solution :Equation of NORMAL at point `P(a SEC THETA, b tan theta)` on HYPERBOLA `(x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1` is

`a cos theta x +b COT theta y =a^(20+b^(2)`
`:. G((a^(2)+b^(2))/(a cos theta),0)`
`S (ae,0)`
`SP = e (a sec theta) -a`
Also `SG =(a^(2)+b^(2))/(a cos theta) -ae =(a^(2)e^(2))/(a cos theta) - ae = e[e(a sec theta)-a]`
`rArr SG//SP = e= 6`


Discussion

No Comment Found

Related InterviewSolutions