InterviewSolution
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InterviewSolution
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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 |
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Answer» 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` |
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