माना की वृत्त C_(1) : x^(2)+y^(2)=9 और वृत्त C_(2) :(x-3)^(2)+(y-4)^(2)=16, एक -दूसरे को बिन्दुओ...

Solve: (x-2)(y-2)=4(y-3)(z-3)=9(z-4)(x-4)=16

Number of common tangents to the circles C_(1):x ^(2) + y ^(2) - 6x - 4y -12=0 and C _(2) : x ^(2) + y ^(2) + 6x + 4y+ 4=0 is

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

Factorise : 16 (2x - y) ^(2) - 24 (4x ^(2) - y ^(2) ) + 9 ( 2x + y) ^(2)

{:("Column" A ,, "Column" B), ((3x^(2) - 5)- (2x^(2) - 5 + y^(2)) ,, (a) x^(2) + xy + y^(2)) , (9x^(2) - 16y^(2) ,, (b) 2) , ((x^(3) - y^(3))/(x-y) ,, (c) (9x + 16y) (9x - 16y)) , ("The degree of " (x + 2) (x+3) ,, (d) x^(2) - y^(2)) , (,, (e) 1) , (,, (f) (3x + 4y) (3x - 4y)):}

Consider the two curves C_(1);y^(2)=4x,C_(2)x^(2)+y^(2)-6x+1=0 then :

Consider two concentric circles C_(1):x^(2)+y^(2)=1 and C_(2):x^(2)+y^(2)-4=0 .A parabola is drawn through the points where c_(1) ,meets the x -axis and having arbitrary tangent of C_(2) as directrix.Then the locus of the focus of drawn parabola is (A) "(3)/(4)x^(2)-y^(2)=3, (B) (3)/(4)x^(2)+y^(2)=3, (C) An ellipse (D) An hyperbola