Let (x, y) be a variable point on the curve 4 x²+9 y²-8 x-36 y+15=0 . Then (x²-2 x+y²-4 y+5 )+ (x²-2 x+y²-4 y+5 ) is -

Step-by-step solution

array l 4 x²+9 y²-8 x-36 y+15=0 4 (x²-2 x )+9 (y²-4 y )=-15 4 (x²-2 x+1 )+9 (y²-4 y+4=-15+4+36 . 4(x-1)²+9(y-2)²=25 (x-1)² ( 5 2 )² + (y-2)² ( 5 3 )² =1 . .(1) x²-2 x+y²-4 y+5 (x-1)²+(y-2)² array of ((x-1)²+(y-2)² )= 25 9 of ((x-1)²+(y-2)² )= 25 4 = 25 9 + 25 4 = 325 36