Let T₁ be the tangent drawn at a point P( 2 , 3 ) on the ellipse x^2 4 + y^2 6 =1 . If ( , ) is the point where T₁ intersects another tangent T₂ to the ellipse perpendicularly, then ^2+ ^2=

Step-by-step solution

Given ellipse x^2 4 + y^2 6 =1 a^2=4, b^2=6 Equation of tangent in slope form is y=m x+ a^2 m^2+b^2 ( , ) lies on it =m + 4 m^2+6 aligned & ^2+m^2 ^2-2 m =4 m^2+6 & m^2 ( ^2-4 )-2 m + ^2-6=0 aligned Tangents are perpendicular m₁ m₂=-1 ^2-6 ^2-4 =-1 ^2+ ^2=10