1) if parabola y2=px passes through point (2,-3),find the length of latus rectum .

2) find the value of p so that the equation x2 +y2 - 2px+ 4y - 12=0 may represent a circle of radius 5 units .

3) one end of the diameter of a circle x2+y2-6x+5y-7=0 os (7,-8).find the co-ordinates of other end

In the given question, we are given a parabola y2=px which passes through the point (2,-3). So, substituting x = 2 and y = -3 in the given equation we get

Now, substituting p=92in the given parabola, we get
y2=92x  ...(1)

Next, comparing equation (1) with the equation of the parabola y2=4ax, we get
4a=92  ...(2)
Now we know that the length of latus rectum is 4a. So, using equation (2)
Length of the latus rectum = 4a
  = 92
Therefore, the length of the latus rectum is 92

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