Question

the angle between the tangents drawn from any point on the circle x2+y2=3 to the hyperbola

Answer 1

The angle between the tangents drawn from any point on the circle x^2+y^2=3 to the hyperbola x^2/4-y^2=1 is?

hyperbola

2 answers · Mathematics 

 Best Answer

Equation to top of circle is y = √(3 - x^2). 
Equation to bottom of hyperbola is y = -√(x^2 - 4) / 2. 

Let tangent1 be the line that meets top of circle (quadrant 1) at P(p, √(3 - p^2)), 
and bottom of hyperbola (quadrant 4) at Q(q, -√(q^2 - 4) / 2). 

The slope of tangent1 is the same as the slope of the circle at P. 
This slope is the derivative of y = √(3 - x^2), which is y' = -x/√(3 - x^2). 
Therefore, slope of tangent1 = m = -p/√(3 - p^2).