InterviewSolution
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InterviewSolution
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The locus a point `P(alpha,beta)` moving under the condition that the line `y=alphax+beta` is a tangent to the hyperbola `x^2/a^2-y^2/b^2=1` isA. a hyperbolaB. a parabolaC. a circleD. an ellipse |
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Answer» If `y=alpha x+beta` touches the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`. ltbtgt then `beta^(2)=a^(2)alpha^(2)-b^(2)` [Putting `c=beta` and `m=alpha` in `c^(2)=a^(2)m^(2)-b^(2)`] Hence, locus of `P(alpha,beta)` is `y^(2)=a^(2)x^(2)-b^(2)` or , `a^(2)x^(2)-y^(2)=b^(2)` which represents a hyperbola. |
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