1)** if parabola y ^{2}=px passes through point (2,-3),find the length of latus rectum .**

*2) find the value of p so that the equation x ^{2} +y^{2} - 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

* *

*x*= 2 and

*y*= -3 in the given equation we get

${\left(-3\right)}^{2}=p\left(2\right)\phantom{\rule{0ex}{0ex}}9=2p\phantom{\rule{0ex}{0ex}}p=\frac{9}{2}$

Now, substituting $p=\frac{9}{2}$in the given parabola, we get

${y}^{2}=\frac{9}{2}x$ ...(1)

Next, comparing equation (1) with the equation of the parabola ${y}^{2}=4ax$, we get

$4a=\frac{9}{2}$ ...(2)

Now we know that the length of latus rectum is 4

*a*. So, using equation (2)

Length of the latus rectum = 4

*a*

= $\frac{9}{2}$

Therefore, the length of the latus rectum is $\frac{9}{2}$

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