If the parabola `y=a x^2-6x+b` passes through `(0,2)` and has its tangent at `x=3/2` parallel to the x-axis, then `a=2,b=-2` (b) `a=2,b=2` `a=-2,b=2` (d) `a=-2,b=-2`

If the curve y=ax^(2)-6x+b pass through (0,2) and has its tangent parallel to the x-axis at x=(3)/(2), then find the values of a and b

If the parabola y=(a-b)x^(2)+(b-c)x+(c-a) touches x -axis then the line ax+by+c=0 passes through a fixed point

y^2=4x-20 ,Tangent to this parabola at (6,2) is also tangent to x^2/2+y^2/b=1 then find b

Parabola y^(2)=x+1 cuts the Y-axis in A and B. The sum of slopes of tangents to the parabola at A and B is

The hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (2, ) and has the eccentricity 2. Then the transverse axis of the hyperbola has the length 1 (b) 3 (c) 2 (d) 4

If a and b are roots of the equation x^2+a x+b=0 , then a+b= (a) 1 (b) 2 (c) -2 (d) -1

The line 3x-2y=24 meets x-axis at A and y-axis at B. The perpendicular bisector of AB meets the line through (0, -1) and parallel to x-axis at C. Then C is: (A) (-7/2,-1) (B) (-15/2,-1) (C) (-11/2,-1) (D) (-13/2,-1)

If (a,b) is the midpoint of a chord passing through the vertex of the parabola y^(2)=4x then a=2b( b) a^(2)=2ba^(2)=2b( d )2a=b^(2)

If x=a sec theta and y=b tan theta, then b^(2)x^(2)-a^(2)y^(2)=( a )ab(b)a^(2)-b^(2)(c)a^(2)+b^(2) (d) a^(2)b^(2)

If the lines x-y=a and x+y=b are tangents for y=x^2-3x+2 then a/b=