# 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 ${y}^{2}=px$ which passes through the point (2,-3). So, substituting 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 4a. So, using equation (2)
Length of the latus rectum = 4a
= $\frac{9}{2}$
Therefore, the length of the latus rectum is $\frac{9}{2}$

"Due to paucity of time it would not be possible for us to solve all your queries. We are providing solution to one of your queries. Try solving the rest of the questions yourself and if you face any difficulty then do get back to us."

• 6
What are you looking for?