JEE PYQ: Circle Question 13
Question 13 - 2021 (26 Feb Shift 2)
Let $A(1, 4)$ and $B(1, -5)$ be two points. Let $P$ be a point on the circle $(x-1)^2 + (y-1)^2 = 1$ such that $(PA)^2 + (PB)^2$ have maximum value, then the points $P$, $A$ and $B$ lie on:
(1) a parabola
(2) a straight line
(3) a hyperbola
(4) an ellipse
Show Answer
Answer: (2)
Solution
$P = (1+\cos\theta, 1+\sin\theta)$. $PA^2 + PB^2 = \cos^2\theta + (3+\sin\theta)^2 + \cos^2\theta + (6-\sin\theta)^2$. Simplifying and maximizing: $\sin\theta = -\frac{3}{2}$… actually max when $\theta = \frac{3\pi}{2}$, giving $P(1,0)$. $P$, $A$, $B$ all have $x = 1$, so they lie on a straight line.
BETA
