`12^(2)+9^(2)=?+108`

Find the equations of the tangent and normal to hyperbola 12x^(2) - 9y^(2) = 108 " at" theta = pi/3 .

The line 5 x+12 y=9 touch the hyperbola x^(2)-9 y^(2)=9 at

Analyze the roots of the following equations: (i) 2x^(3) - 9x^(2) + 12x - (9//2) = 0 (ii) 2x^(3) - 9x^(2) + 12x - 3 = 0

The normal to the curve 2x^(2)+y^(2)=12 at the point (2,2) cuts the curve again at (A)(-(22)/(9),-(2)/(9)) (B) ((22)/(9),(2)/(9))(C)(-2,-2)(D) none of these

Fill in the blanks. 9 xx (-12) = ? = - 108

(12^2-4^2)/(9^2-3^2) =?

Factorise : (ii) a^(2) - 23 a - 108