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6.

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is 


A) 43

B) 43

C) 23

D) 3



7.

Let P be the point on the parabola, y2=8x, which is a minimum distance from the centre  C of the circle,  x^{2}+(y+6)^{2}=1 Then, the equation of the circle passing through C and having its centre at P is


A) x^{2}+y^{2}-4x+8y+12=0

B) x^{2}+y^{2}-x+4y-12=0

C) x^{2}+y^{2}-8x+8y+19=0

D) x^{2}+y^{2}-4x+9y+18=0



8.

If one of the diameters of the circle, given by the equation  x^{2}+y^{2}-4x+6y-12=0, is a chord of a circle S, whose centre is at (-3,2), then the radius of S is


A) 5\sqrt{2}

B) 5\sqrt{3}

C) 5

D) 10



9.

Two sides of a rhombus are along the lines, x-y+1=0 and 7x-y-5=0. If its diagonals interset at (-1,-2)  then which one of the following is a vertex of this rhombus?


A) (-3,-9)

B) (-3,-8)

C) (\frac{1}{3},-\frac{8}{3})

D) (-\frac{10}{3},-\frac{7}{3})



10.

 If curve y=f(x) passes through the point (1,-1) and satisfies the differential equation

y(1+xy)dx=xdy , then f(-1/2) is equal to 


A) -\frac{2}{5}

B) -\frac{4}{5}

C) \frac{2}{5}

D) \frac{4}{5}



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