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Find the equation of pair of tangents drawn from point (4, 3) to the hyperbola `(x^(2))/(16)-(y^(2))/(9)=1`. Also, find the angle between the tangents. |
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Answer» Equation of pair of tengents is `T^(2)=SS_(1)`. `therefore" "((4x)/(16)-(3y)/(9)-1)^(2)=((x^(2))/(16)-(y^(2))/(9)-1)(-1)` `rArr" "(x^(2))/(16)+(y^(2))/(9)+1-(xy)/(6)-(x)/(2)+(2y)/(3)=-(x^(2))/(16)+(y^(2))/(9)+1` `rArr" "(x^(2))/(8)-(xy)/(6)-(x)/(2)+(2y)/(3)=0` `rArr 3x^(2)-4xy-12x+16y=0,` which is requird equation of pair of tangents. Comparing it with standard second-degree equation, we have `a=3,b=0 and h=-2` `therefore` Angle between tangents, `theta=tan^(-1).(2sqrt(h^(2)-ab))/(|a+b|)` `=tan^(-1).(2sqrt((-2)^(2)-(3)(0)))/(|3+0|)` `=tan^(-1).(4)/(3)` |
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