Answer Verified Hence, considering the general point of contact for both the ellipses can be given as,\[(\dfrac{{{a^2}}}{3},\dfrac{{{b^2}}}{3})\]and for another ellipse point of contact will be given as \[(\dfrac{{{A^2}}}{3},\dfrac{{{B^2}}}{3})\].Now, considering the condition for circle and the straight line as,The equation of straight line is \[x + y = 3\]and the centre of circle is \[(0,1)\]Calculating their point of intersection of the circle and straight line,Diagram of the circle and straight line:
Hence from (1) and (2), we have that Option (A) and (B) are correct. Note: In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. As such, it generalizes a circle, which is the special type of ellipse in which the two focal points are the same. A circle is a shape consisting of all points in a plane that are a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.In geometry, the notion of line or straight line was introduced by ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects, which are often described in terms of two points or referred to using a single letter.> Suggest Corrections 0
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