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Two tangents are drawn to the hyperbola `x^2/a^2-y^2/b^2=1` such that product of their slope is `c^2` . the locus of the point of intersection isA. `x^(2)-a^(2)=c^(2)(y^(2)+b^(2))`B. `x^(2)+a^(2)=c^(2)(y^(2)-b^(2))`C. `y^(2)+b^(2)=c^(2)(x^(2)-a^(2))`D. None of these |
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Answer» Correct Answer - 3 Equation of tangent in the slope form is `y=mx pm sqrt(a^(2)m^(2)-b^(2))` Let the tangents be drawn from (h,K) `thereforek=mh" "sqrt(a^(2)m^(2)-b^(2))` `rArr(h^(2)-a^(2)m^(2)-2hkm+(k^(2)+b^(2))=0-(i)` Let it roots are `m_(1)" and "m_(2)` `rArr m_(1)m_(2)=a^(2)` `rArr(k^(2)+b^(2))/(h^(2)-a^(2))e^(2)` `therefore"locus"(x^(2)-y^(2))c^(2)=y^(2)=b^(2)` |
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