Question

The length of the latus rectum of the parabola 9x2 – 6x + 36y + 19 = 0 is

Solution

Correct option is

4

9x2 – 6x + 36y + 19 = 0      9x2 – 6x = –36y ­– 19 

   (3x – 1)2 = –18(2y + 1)

  

 x2 = – 4a y type

So latus rectum = 4.

 

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

The equation of common tangent to the curves y2 = 8x and xy = –1 is

Q4

From the point (–1, 2) tangent lines are drawn to the parabola y2 = 4x, then the equation of chord of contact is

Q5

For the above problem, the area of triangle formed by chord of contact and the tangents is given by

Q6

A point moves on the parabola y2 = 4ax. Its distance from the focus is minimum for the following value(s) of x.

Q7

The line x – y + 2 = 0 touches the parabola y2 = 8x at the point

Q8

If t is the parameter for one end of a focal chord of the parabola y2 = 4ax, then its length is

Q9

The point on the parabola y2 = 8x at which the normal is inclined at 600 to the x-axis has the coordinates

Q10

The equation of a circle passing through the vertex the extremities of the latus rectum of the parabola y2 = 8x  is