The equations of lines are given by $$sin$$θ$$x+a=1+$$$$cos$$θy, $$sin$$θx−$$a=$$−$$1$$−$$cos$$θy. The locus of point of intersection of lines is $$xm+yn=al$$ then $$l+m+n$$ is

Question

The equations of lines are given by  $$sin$$θ$$x+a=1+$$$$cos$$θy, $$sin$$θx−$$a=$$−$$1$$−$$cos$$θy. The locus of point of intersection of lines is $$xm+yn=al$$ then $$l+m+n$$ is

Infinity Learn · Accepted Answer

Locus of point of intersection of two lines having parameter $θ$ , is the equation obtained by eliminating $θ$ from both equations

$\frac{x + a}{y} = \frac{1 + cosθ}{sinθ}$

And
$\frac{x - a}{y} = - \frac{1 - cosθ}{sinθ}$
Multiply both equations
$\begin{matrix} \frac{x + a}{y} \cdot \frac{x - a}{y} = - (\frac{1 + cosθ}{sinθ}) \cdot (\frac{1 - cosθ}{sinθ}) \\ \frac{x^{2} - a^{2}}{y^{2}} = - \frac{1 - \cos^{2} θ}{\sin^{2} θ} \\ = - 1 \\ x^{2} - a^{2} = - y^{2} \\ x^{2} + y^{2} = a^{2} \end{matrix}$

Here $l = m = n = 2$ ,
Therefore, $l + m + n = 6$

Equation of line in Straight lines

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The equations of lines are given by $sinθ (x + a) = (1 + cosθ) y$ , $sinθ (x - a) = - (1 - cosθ) y$ . The locus of point of intersection of lines is $x^{m} + y^{n} = a^{l}$ then $l + m + n$ is

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Equation of line in Straight lines

Remember concepts with our Masterclasses.

The equations of lines are given by sinθx+a=1+cosθy, sinθx−a=−1−cosθy. The locus of point of intersection of lines is xm+yn=al then l+m+n is

Ready to Test Your Skills?

free study material

The equations of lines are given by $sinθ (x + a) = (1 + cosθ) y$ , $sinθ (x - a) = - (1 - cosθ) y$ . The locus of point of intersection of lines is $x^{m} + y^{n} = a^{l}$ then $l + m + n$ is