The length of the latus rectum of the parabola 9x2 – 6x + 36y + 19 = 0 is
9x2 – 6x + 36y + 19 = 0 9x2 – 6x = –36y – 19
(3x – 1)2 = –18(2y + 1)
x2 = – 4a y type
So latus rectum = 4.
Through the vertex O of parabola y2 = 4x, chords OP and OQ are drawn at right angles to one another. The locus of the middle point of PQ is
The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix
The equation of common tangent to the curves y2 = 8x and xy = –1 is
From the point (–1, 2) tangent lines are drawn to the parabola y2 = 4x, then the equation of chord of contact is
For the above problem, the area of triangle formed by chord of contact and the tangents is given by
A point moves on the parabola y2 = 4ax. Its distance from the focus is minimum for the following value(s) of x.
The line x – y + 2 = 0 touches the parabola y2 = 8x at the point
If t is the parameter for one end of a focal chord of the parabola y2 = 4ax, then its length is
The point on the parabola y2 = 8x at which the normal is inclined at 600 to the x-axis has the coordinates
The equation of a circle passing through the vertex the extremities of the latus rectum of the parabola y2 = 8x is