if a is equals to 1 to 20 equals to 2 - 3 and c is equals to minus 23 are the points a point p such that p a square + b square is equals to 2 PC square then show that the equation to the locus of p is 7 x minus 7 by + 4 is equal to zero
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Let P = (x, y) given condition is PA2 + PB2 = 2c2 => (x – a)2 + (y – 0)2 + (x + a)2 + (y – 0)2 = 2c2 => x2 + a2 – 2xa + y2 + x2 + a2 + 2xa + y2 = 2c2 => 2x2 + 2y2 + 2a2 = 2c2 => x2 + y2 = c2 – a2. => The locus of P is x2 + y2 = c2 – a2
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