For all real values of `m ,` the straight line `y=m x+sqrt(9m^2-4)` is a tangent to which of the following certain hyperbolas? (a)`9x^2+4y^2=36` (b) `4x^2+9y^2=36` (c)`9x^2-4y^2=36` (d) `4x^2-9y^2=36`

Which of the following line can be tangent to the parabola y^2=8x ? (a) x-y+2=0 (b) 9x-3y+2=0 (c) x+2y+8=0 (d) x+3y+12=0

Which of the following line can be normal to parabola y^2=12 x ? (a) x+y-9=0 (b) 2x-y-32=0 (c) 2x+y-36=0 (d) 3x-y-72=0

Find the vertices of the hyperbola 9x^2-16 y^2-36 x+96 y-252=0

Identify the type of conic for the following equation. 9x^(2)-4y^(2)-18x+8y-25=0

Identify the type of conic section for each of the following equations: 4x^(2)-9y^(2)=36

If y=4x+c is a tangent to the circle x^(2)+y^(2)=9 , find c.

The equation of the transvers axis of the hyperbola (x-3)^2+(y=1)^2+(4x+3y)^2 is x+3y=0 (b) 4x+3y=9 3x-4y=13 (d) 4x+3y=0

Let P and Q be any two points on the lines represented by 2x-3y = 0 and 2x + 3y = 0 respectively. If the area of triangle OPQ (where O is origin) is 5, then which of the following is not the possible equation of the locus of mid-point of PO? (a) 4x^2-9y^2 +30 = 0 (b) 4x^2-9y^2-30 = 0 (c) 9x^2-4y^2-30=0 (d) none of these

Find the value of c if y = x + c is a tangent to the hyperbola 9x^(2) -16y^(2) = 144

Identify the type of the conic for the following equations: 1. 16y^(2)=-4x^(2)+64 2. x^(2)+y^(2)=-4x-y+4 3. x^(2)-2y=x+3 4. 4x^(2)-9y^(2)-16x+18y-29=0