First slide

Definition of a circle

Question

The tangent at any point to the circle $x^{2} + y^{2} = r^{2}$ meets the coordinate axes at A and B. If the lines drawn parallel to the coordinate axes through A & B intersect at P. Then the locus of P is

Moderate

A

$x^{2} + y^{2} = r^{- 2}$
B

$x^{- 2} + y^{- 2} = r^{2}$
C

$x^{- 2} + y^{- 2} = r^{- 2}$
D

$x^{- 2} - y^{- 2} = r^{- 2}$

Solution

$Equation of tangent at R (r \cos θ, r \sin θ) is x \cos θ + y \sin θ = r - - - - (1)$
$A (\frac{r}{\cos θ}, 0), B (0, \frac{r}{\sin θ})$
$\begin{array}{l} Let P (h, k) then h = \frac{r}{\cos θ}, k = \frac{r}{\sin θ} \\ \cos θ = \frac{r}{h}, \sin θ = \frac{r}{k} \\ ∴ 1 = r^{2} (\frac{1}{h^{2}} + \frac{1}{k^{2}}) \\ Required locus x^{- 2} + y^{- 2} = r^{- 2} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App