Question

The locus of the point (h,k) from which the tangent can be drawn to the different branches of the hyperbola

x²/a² - y²/b² = 1 is

A. k²/b² - h²/a² < 0
B. k²/b² - h²/a² = 0
C. k²/b² - h²/a² >0
D. none of these

Answer 1

The locus of the point (h,k) from which the tangent can be drawn to the different branches of the hyperbola x²/a² - y²/b² = 1 is k²/b² - h²/a² < 0.

Step-by-step explanation:

The locus of the point (h,k) from which the tangent can be drawn to the different branches of the hyperbola x²/a² - y²/b² = 1 can be determined by the inequality k²/b² - h²/a² < 0.

To understand this, let's consider the equation of a hyperbola in standard form: (x²/a²) - (y²/b²) = 1. In order for a point (h,k) to lie on the hyperbola, it must satisfy this equation.

Now, for a point (h,k) to be able to draw tangents to the different branches of the hyperbola, it must lie outside the hyperbola but within the distance of the transverse axis.