Find the pole of the straight line x = 2y = 1 with respect to the circle $x^{2} + y^{2} = 5 .$

Open in App

Solution

The straight line given is $x + 2 y = 1$

Let $(x_{1}, y_{1})$ be the pole of the line

Using formula for polar,

$x x_{1} + y y_{1} = 5$

Comparing with the given line,
$\frac{x_{1}}{1} = \frac{y_{1}}{2} = \frac{5}{1}$

Hence, $x_{1} = 5$ and $y_{1} = 10$

ANSWER: $(5, 10)$

Suggest Corrections

Similar questions

x + 2 y = 1

x^{2} + y^{2} = 5

x^{2} + y^{2} - 4 x + 3 y - 1 = 0 .

48 x + 54 y + 53 = 0

x^{2} + y^{2} - 4 x + 3 y - 1 = 0

x + 2 y = 1

x^{2} + y^{2} = 5

a x + b y + 3 a^{2} + 3 b^{2} = 0

x^{2} + y^{2} + 2 a x + 2 b y = a^{2} + b^{2} .

Join BYJU'S Learning Program