Parabola Test -...

If the tangents at two points (1, 2) and (3, 6) as a parabola intersect at the point (– 1, 1), then the slope of the directrix of the parabola is 

A variable chord PQ of the parabola y = 4x² substends a right angle at the vertex. Then the locus of points of intersection of the tangents at P and Q is

Point on the curve y² = 4(x- 10) which is nearest to the line x + y = 4 may be

If (h, k) is a point on the axis of parabola 2(x -1)² + 2 (y -1)² = (x + y + 2)² from where three distinct normals can be drawn, then

The equation of the common tangent touching the circle (x – 3)² + y² = 9 and the parabola y² = 4x below y² - 4x below the x–axis is 

The line x + y = 6 is a normal to the parabola y² = 8x at the point

The tangent and normal at the point P(4, 4) to the parabola, y² = 4x intersect the x–axis at the points Q and R respectively. Then the cirucm centre of the ΔPQR is

All chords of the parabola y² = 4x which subtend right angle at the origin are concurrent at the point:

The mirror image of the parabola y² = 4x in the tangent to the parabola to the point (1,2) is

The locus of mid–point of family of chords λx + y - 5 = 0 (parameter) of the parabola x² = 20y is