Conic Section T...

If two tangents drawn from the point (α, β) to the parabola y² = 4x be such that the slope of one tangent is double of the other, then

y + h = m₁(x + a) and y + k = m₂ (x + a) are two tangents to the parabola y² = 4ax ; then

The area of the triangle formed by the tangent and the normal to the parabola y² = 4ax, both drawn at the same end of the latus rectum and the axis of the parabola is

Let P, Q, R be three pts. on a parabola, normals at which are concurrent. The centroid of the ∆ PQR must lie on

The vertex of the parabola y² = 8x is at the centre of a circle and the parabola cuts the circle at the ends the latus rectum. Then the equation of the circle is

If O is the pole of the chord PQ of a parabola, then the perpendicular from P, O, Q on any tangent to the curve are in

The ends of a line segment are P (1, 3) and Q (1, 1). R is a point on the line segment PQ such that PR : RQ = 1 : λ. If R is an interior point of the parabola y² = 4x , then

The equation of the conic with focus at (1, –1), directrix along x – y = 0 and with eccentricity √2 is