The locus of the $$mid-point$$ of the portion intercepted between the axes by the line x $$cos$$ a $$+$$ y $$sin$$ a $$=$$ p, where p is a constant, is

Question

The locus of the $$mid-point$$ of the portion intercepted between the axes by the line x $$cos$$ a $$+$$ y $$sin$$ a $$=$$ p, where p is a constant, is

Infinity Learn · Accepted Answer

The line xcos⁡α$$+ysin$$⁡α$$=p$$ meets the coordinate axes at Aμ$$cos$$⁡α,$$0$$ and $$B0$$,psin⁡α. Let (h$$, $$k) be the coordinates of the mid point of the portion AB intercepted between the axes by the line x $$cos$$ $$a+$$ y $$sin$$ $$od=p$$.$$Thenph=$$$$cos$$⁡α$$2$$,$$k=0+$$$$sin$$⁡α$$2$$⇒ $$cos$$⁡α$$=p2h$$,$$sin$$⁡α$$=p2k$$⇒ $$cos2$$⁡α$$+sin2$$⁡α$$=p24h2+p24k2$$⇒ $$p24h2+p24k2=1Hence$$, the locus of (h$$, $$k) $$isp24x2+p24y2=1$$ or, $$1x2+1y2=tp2$$

The locus of the mid-point of the portion intercepted between the axes by the line x cos $a + y$ sin $a = p$ , where $p$ is a constant, is

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The locus of the mid-point of the portion intercepted between the axes by the line x cos a + y sin a = p, where p is a constant, is

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The locus of the mid-point of the portion intercepted between the axes by the line x cos $a + y$ sin $a = p$ , where $p$ is a constant, is