The given ellipse is x2/6 + y2/3 = 1
and every point on it is of the form P(√6cosθ , √3 sinθ). The nearest point on the ellipse is the point at which the normal to the ellipse is perpendicular to the line x + y - 7 = 0 or equivalently, the tangent is parallel to the .The tangent at P(√6cosθ , √3 sinθ) is
xcosθ/√6 + ysinθ/√3 = 1
whose slope is given by
Therefore, the nearest point in the first quadrant is
