All Chords Of The Curve 3x2 – Y2 –2x + 4y = 0 That Subtends A Right Angle At The Origin, Pass Through A Fixed Point Whose Co-ordinate Is –

The line x + y = 1 meets the line represented by the equation y³ –xy² – 14x²y + 24x³ = 0 at the points A, B, C. If O is the origin, then

OA² + OB² + OC² is equal to    

If the area of the triangle formed by the pair of lines 8x² – 6xy + y² = 0 and the line 2x + 3y = a is 7, then a is equal to

If p is length of the perpendicular from the origin on the line  are in A.P. then ab is equal to  

If two of the lines given by the equation ax³ – 9yx² – y²x + 4y³ = 0 are perpendicular then a is equal to

The number of straight lines equidistant from three non-collinear points in the plane of the points is equal to

A line bisecting the ordinate PN of a point P(at², 2at), t > 0 on the parabola y2 = 4ax, a > 0 is drawn parallel to the axis to meet the curve at Q. If NQ and the tangent at the point P meet at, T, then the coordinates of point T is (where point N lie on the axis)

If the pair of line  intersect on x-axis, then α is equal to –

If the area of the rhombus enclosed by the lines  be 2 square units, then

If a² + b² – c² – 2ab = 0 then the point of concurrency of family of straight lines ax + by + c = 0lies on the line –

In a triangle ABC,  and point A lies on line y = 2x + 3 where  Area of  is such that [∆] = 5. Possible co-ordinates of ∆ is/are –