First slide

Equation of line in Straight lines

Question

The locus of the point of intersection of lines $x \cos α + y \sin α = a and x \sin α - y \cos α = b (α$ is a variable), is

Moderate

A

$2 (x^{2} + y^{2}) = a^{2} + b^{2}$
B

$x^{2} - y^{2} = a^{2} - b^{2}$
C

$x^{2} + y^{2} = a^{2} + b^{2}$
D

none of these

Solution

Let (h, k) be the point of intersection of the line $x \cos α + y \sin α = a and x \sin α - y \cos α = b .$ Then,
$h \cos α + k \sin α = a$
$h \sin α - k \cos α = b$
Squaring and adding (i) and (ii), we get
$\begin{array}{l} (h \cos α + k \sin α)^{2} + (h \sin α - k \cos α)^{2} = a^{2} + b^{2} \\ h^{2} + k^{2} = u^{2} + b^{2} \end{array}$
Hence, $(h, k) is x^{2} + y^{2} = a^{2} + b^{2}$

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