1. Tardigrade
  2. Question
  3. Mathematics
  4. If a point P has co-ordinates (0, -2) and Q is any point on the circle, x2 + y2 - 5x - y + 5 = 0, then the maximum value of (PQ)2 is :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If a point P has co-ordinates $(0, -2)$ and Q is any point on the circle, $x^2 + y^2 - 5x - y + 5 = 0$, then the maximum value of $(PQ)^2$ is :

JEE MainJEE Main 2017Conic Sections

Solution:

$\left(x-5/2\right)^{2} \frac{-25}{4}+\left(y-1/2\right)^{2} - 1/4+5 = 0$
$= \left(x - 5/2\right)^{2} + \left(y -1/2\right)^{2} = 3/2$
on circle Q $= 5/2 +\sqrt{3/ 2}cos \,Q, \frac{1}{2}+\sqrt{3/ 2} sin\, Q$
$PQ^{2} = \left(\frac{5}{2}+\sqrt{3/ 2}cos\,Q\right)^{2}+\left(\frac{5}{2}+\sqrt{3/ 2}sin Q\right)^{2}$
$PQ^{2} = \frac{25}{2}+\frac{3}{2}+5\sqrt{3/ 2}\left(cos \,Q+sin \,Q\right)$
$man^{mr} = 14+5\sqrt{3/ 2}\left(\sqrt{2}\right)$
$= 14+5\sqrt{3}$