A tangent drawn to hyperbola x^2a^2-y^2b^2=1 at P(π)/6 forms a triangle of area 3a^2 square units, with coordinate axes. If the eccentricity of…

Question

A tangent drawn to hyperbola x^2a^2-y^2b^2=1 at P(π)/6 forms a triangle of area 3a^2 square units, with coordinate axes. If the eccentricity of hyperbola is e, then the value of e^2-9 is

MARKS Content Team · Accepted Answer

Correct answer: (D) 8. The point P(π)/6 is asec(π)/6,btan(π)/6 or P(2a√3,b√3∴ Equation of tangent at P is x√3a)/2-y/(√3b)=11$ ∴ Area of the triangle =1/2×(√3a)/2×√3b=3a^2 ∴ b/a=4 e^2=1+b^2a^2=17 Now, e^2-9=17-9=8 Hence, option (d) is correct.

A tangent drawn to hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ at $P (\frac{π}{6})$ forms a triangle of area $3 a^{2}$ square units, with coordinate axes. If the eccentricity of hyperbola is $e$ , then the value of $e^{2} - 9$ is

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More Hyperbola Questions

A tangent drawn to hyperbola x2a2-y2b2=1 at Pπ6 forms a triangle of area 3a2 square units, with coordinate axes. If the eccentricity of hyperbola is e, then the value of e2-9 is

Solution

More Hyperbola Questions

A tangent drawn to hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ at $P (\frac{π}{6})$ forms a triangle of area $3 a^{2}$ square units, with coordinate axes. If the eccentricity of hyperbola is $e$ , then the value of $e^{2} - 9$ is