First slide

Equation of line in Straight lines

Question

If A and B are two fixed points, then the locus of a point which moves in such a way that the angle APB is a right angle, is

Moderate

A

a circle
B

an ellipse
C

a parabola
D

none of these

Solution

Let $A (x_{1}, y_{1}), B (x_{2}, y_{2})$ be two fixed points and
let $P (h, k)$ be a variable point such that $∠ A P B = \frac{π}{2} \cdot$ Then,
Slope of $A P \times$ Slope of BP = $- 1$
$\Rightarrow (h - x_{1}) (h - x_{2}) + (k - y / 1) (k - y_{2}) = 0$
Hence, the locus of $(h, k)$ is
$(x - x_{1}) (x - x_{2}) + (y - y_{1}) (y - y_{2}) = 0$ which is a circle
having $A B$ as diameter

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