Tangents are drawn from a point `P(6,sqrt(5))` to the ellipse `x^2/25+y^2/16=1`touching the ellipse in the points Q and R. The angle between PQ and PR is

Explanation

Equation of tangent to an ellipse=>`y=mx+-sqrt(a^2 m^2+b^2)`.

here `a^2=25 and b^2=16`

substituting values we get=>` y=mx+-sqrt(25 m^2+16)` the point `(6,sqrt5)`, will satisfy this equation,so substituting values of x and y we get the eqn=>

`11m^2 -12sqrt(5)m-11=0`

using quadratic formula we get two values of m

`m_1=(6sqrt(5)+sqrt(301))/(11) m_2=(6sqrt(5)-sqrt(301))/(11)`

angle between the two tangents=`theta=tan^(-1)((m_1-m_2)/(1+m_1m_2))`

substituting values of m_1 and m_2 we get=> `theta=.tan^(-1)oo=pi/2`