The normal to a curve at P(x, y) meets the x-axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is a

• ellipse

• parabola

• circle

• hyperbola

A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at 

Consider a family of circles which are passing through the point (-1, 1) and are tangent to x-axis. If (h, K) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interva

The equation of a tangent to the parabola y² = 8x is y = x + 2. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

In an ellipse, the distance between its foci is 6 and minor axis is 8. Then its eccentricity is

If the lines 3x − 4y − 7 = 0 and 2x − 3y − 5 = 0 are two diameters of a circle of area 49π square units, the equation of the circle is