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Let `S`be the circle in the `x y`-plane defined by the equation `x^2+y^2=4.`(For Ques. No 15 and 16)Let `P`be a point on the circle `S`with both coordinates being positive. Let the tangentto `S`at `P`intersect the coordinate axes at the points `M`and `N`. Then, the mid-point of the line segment `M N`must lie on the curve`(x+y)^2=3x y`(b) `x^(2//3)+y^(2//3)=2^(4//3)`(c) `x^2+y^2=2x y`(d) `x^2+y^2=x^2y^2`A. `(x+y)^(2) = 3xy`B. `x^(2//3)+y^(2//3) =2^(4//3)`C. `x^(2)+y^(2)=2xy`D. `x^(2)+y^(2)=x^(2)y^(2)` |
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Answer» Correct Answer - 4 Let the coordinates of P be `(2 cos theta , 2 sin theta )` Equation of tangent to circle at P is `x cos x + y sin theta =2` `:. M((2)/(cos theta ,0)),N(0,(2)/(cos theta))` Let the mid -point of MN be `(x,y)` `:. x= (1)/(cos theta ) ` and `y = (1)/(sin theta)` Squaring and adding , we get `(1)/(x^(2))+(1)/(y^(2))=1 ` or `x^(2)+y^(2)=x^(2)y^(2)`, this is the required locus |
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