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Acute angle between two curve `x^(2)+y^(2)=a^(2)sqrt2` and `x^(2)-y^(2)=a^(2)` isA. `(pi)/(6)`B. `(pi)/(3)`C. `(pi)/(4)`D. none of these |
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Answer» Correct Answer - C `x^(2)+y^(2)=a^(2)sqrt2 and x^(2)-y^(2)=a^(2)` `therefore" "(dy)/(dx)=(-x)/(y),(dy)/(dx)=(x)/(y)` Angle between curves is given by `theta=|tan^(-1).((x)/(y)+(x)/(y))/(1-(x^(2))/(y^(2)))|` `=|tan^(-1).(2xy)/(y^(2)-x^(2))|` Squaring and subtracting the equations of given curves, `4x^(2)y^(2)=a^(4)` `therefore" "2xy= pm a^(2)` `therefore" "theta=|tan^(-1).(a^(2))/(a^(2))|` `=tan^(-1)(1)` `=(pi)/(4)` |
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