`P` is a point on positive x-axis, `Q` is a point on the positive y-axis and `' O '` is the origin. If the line passing through `P\ a n d\ Q` is tangent to the curve `y=3-x^2` then find the minimum area of the triangle `O P Q` , is 3 (b) 4 (c) 5 (c) 6

Explanation

the given equation is `y=3- x^2`

let the points be `(t, 3-t^2)`

slope of the tangent is `(dy)/(dx)= -2x = -2t `

equation of tangent `y- y_1 = m(x- x_1)`

`y- (3-t^2) = -2t(x-t)`

`y - 3 + t^2 = -2tx + 2t^2`

`2tx + y-3 = t^2`

`2tx + y = t^2 + 3`

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