From a point P, two tangents PA and PB are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1. If the product of the slopes of these tangents is 1, then…

Question

From a point P, two tangents PA and PB are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1. If the product of the slopes of these tangents is 1, then the locus of P is a conic whose eccentricity is equal to

MARKS Content Team · Accepted Answer

Correct answer: (C) √2. Let, P be h,k and the equation of tangent through P on the hyperbola is y=mx±√(a^2m^2-b^2) ⇒k^2-mh2=a^2m^2-b^2 ⇒h^2-a^2m^2-2khm+k^2+b^2=0 where roots are m_1 and m_2 ⇒(k^2+b^2)/(h^2-a^2)=1=m_1m_2 ⇒ locus is x^2-y^2=a^2+b^2 ⇒ eccentricity =√(1+1)=√2

From a point $P,$ two tangents $P A$ and $P B$ are drawn to the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ . If the product of the slopes of these tangents is $1,$ then the locus of $P$ is a conic whose eccentricity is equal to

Solution

More Hyperbola Questions

From a point P, two tangents PA and PB are drawn to the hyperbola x2a2-y2b2=1. If the product of the slopes of these tangents is 1, then the locus of P is a conic whose eccentricity is equal to

Solution

More Hyperbola Questions

From a point $P,$ two tangents $P A$ and $P B$ are drawn to the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ . If the product of the slopes of these tangents is $1,$ then the locus of $P$ is a conic whose eccentricity is equal to