4^(x^(2)+2)-9*2^(x^(2)+2)+8=0

The eccentricity of the hyperbola 4x^(2) - 9y^(2) - 8x - 32 = 0 is

The length of the transverse axis of the hyperbola 4x^(2) -9y^(2) +8x + 40 =0 is

Evaluate: (lim)_(x rarr0)(8)/(x^(8)){1-cos((x^(2))/(2))-cos((x^(2))/(4))+cos((x^(2))/(2))cos((x^(2))/(4))}

Without solving , comment upon the nature of roots of each of the following equations : (i) 7x^(2)-9x+2=0 (ii) 6x^(2)-13x+4=0 (iii) 25x^(2)-10x+1=0 (iv) x^(2)+2sqrt(3)x-9=0 (v) x^(2)-ax-b^(2)=0 (vi) 2x^(2)+8x+9=0

Find the eccentricity, length of latus rectum, centre, foci, vertices and the equatioin to the dircctriccs of the hyperola. (i) 4x^(2)-5y^(2)-16x+10y+31=0 (ii) 5x^(2)-4y^(2)+20x+8y-4=0 (iii) 4(y+3)^(2)-9(x-2)^(2)=1 (iv) 4x^(2)-9y^(2)-8x-32=0

Irrational roots of the equaiton 2x^(4) + 9x^(3) + 8x^(2) + 9x + 2 = 0 are