गुणनखंड: 4(2x-3y)^(2) - 8x + 12y -3 | 9 | फ़ैक्टरीकरण | गणित | आईसीएसई | संशय

3x^(2) + 8x +4=0, 4y^(2)-19y + 12=0

2 x + 3y = 4, 4x + 6y = 12 .

12xy (9x ^ (2) -16y ^ (2)) -: 4xy (3x + 4y)

1 + 5x + 3y = 9 2x 3y = 12 X = (x, y) - 4

If the equation a^(2) x^(2) + (a^(2) - 5a + 4) xy + (3a - 2) y^(2) - 8x + 12y - 4 = 0 represents a circle , then : a =

(x + y - 8) /( 2 ) = ( x + 2y - 14 ) /( 3) = ( 3x + y - 12)/( 11)

(i) Find the equation of a circle , which is concentric with the circle x^(2) + y^(2) - 6x + 12y + 15 = 0 and of double its radius. (ii) Find the equation of a circle , which is concentric with the circle x^(2) + y^(2) - 2x - 4y + 1 = 0 and whose radius is 5. (iii) Find the equation of the cricle concentric with x^(2) + y^(2) - 4x - 6y - 3 = 0 and which touches the y-axis. (iv) find the equation of a circle passing through the centre of the circle x^(2) + y^(2) + 8x + 10y - 7 = 0 and concentric with the circle 2x^(2) + 2y^(2) - 8x - 12y - 9 = 0 . (v) Find the equation of the circle concentric with the circle x^(2) + y^(2) + 4x - 8y - 6 = 0 and having radius double of its radius.

If P_(1), P_(2), P_(3) are the perimeters of the three circles. S_(1) : x^(2) + y^(2) + 8x - 6y = 0 S_(2) , 4x^(2) + 4y^(2) -4x - 12y - 186 = 0 and S_(3) : x^(2) + y^(2) -6x + 6y - 9 = 0 repeectively, then the relation amongst P_(1), P_(2) and P_(3) is .............