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Find the angle between the pair of tange...

Find the angle between the pair of tangents from the point (1,2) to the ellipse `3x^2+2y^2=5.`

Text Solution

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The combined eqution of the pair of tangents drawn from (1,2) ot the ellipse `3x^(2)+2y^(2)=5` is `(3x+4y-5)^(2)=(3x^(2)+3y^(2)-5)(3+8-5)[ "Using" T^(2)=SS_(1)]`
`or 9x^(2)-24xy-4y^(2)+.....=0`
If angle between pair of lines is `theta`, then
`tan theta=(2sqrt(h^(2)-ab))/(a+b)` where a=9,h12, b=-4
`:. tan theta =(12)/(sqrt(5))`
`rArr theta = tan^(-1).(12)/(sqrt(5))`
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