CBSE Class 12-science Answered

answer

Asked by vinethabairaboina | 24 Sep, 2020, 04:11: PM

Expert Answer

Question:

P is a point which moves in xy-plane, such that the point P is nearer to the centre of a square than any of the sides. The four vertices of the square are (±a, ±a). The region in which P will move is bounded by parts of the parabola of which one has the equation:

Solution:

Let P(x, y)

According to the question,

$square root of straight x squared plus straight y squared end root less or equal than vertical line straight a plus straight x vertical line comma space space square root of straight x squared plus straight y squared end root less or equal than vertical line straight a minus straight x vertical line comma space space square root of straight x squared plus straight y squared end root less or equal than vertical line straight a plus straight y vertical line comma space space square root of straight x squared plus straight y squared end root less or equal than vertical line straight a minus straight y vertical line Therefore comma space the space region space bounded space by space the space curves straight x squared plus straight y squared equals left parenthesis straight a plus straight x right parenthesis squared space rightwards double arrow straight y to the power of 2 end exponent equals straight a squared plus 2 ax straight x squared plus straight y squared equals left parenthesis straight a minus straight x right parenthesis squared space rightwards double arrow straight y squared equals straight a squared minus 2 ax straight x squared plus straight y squared equals left parenthesis straight a plus straight y right parenthesis squared space rightwards double arrow straight x to the power of 2 end exponent equals straight a squared plus 2 ay straight x squared plus straight y squared equals left parenthesis straight a minus straight y right parenthesis squared space rightwards double arrow straight x to the power of 2 end exponent equals straight a squared minus 2 ay$