If ‘$ heta$’ is the angle between the lines ${ax}^{2} + 2hxy + {by}^{2} = 0,\$then angle between $x^{2} + 2xysec\ heta + y^{2} = 0$ is

Question

If ‘$	heta$’ is the angle between the lines ${ax}^{2} + 2hxy + {by}^{2} = 0,\$then angle between $x^{2} + 2xysec\ 	heta + y^{2} = 0$ is

Dr. Abubacker · Accepted Answer

(a)
Angle between the lines ${ax}^{2} + 2hxy + {by}^{2} = 0$ is
$	an	heta = \left| \frac{2\sqrt{h^{2} - ab}}{a + b} ight|$
For $x^{2} + 2xy\sec	heta + y^{2} = 0$
$h = \sec	heta,\ a = b = 1$
$	herefore\ 	an\phi = \left| \frac{2\sqrt{\sec^{2}	heta - 1}}{1 + 1} ight|$
$= \frac{2	an	heta}{2} = 	an	heta$
$	herefore$ Angle between $x^{2} + 2xy\sec	heta + y^{2} = 0\ is\ 	heta$

Q. If ‘$\theta$’ is the angle between the lines ${ax}^{2} + 2hxy + {by}^{2} = 0,\$then angle between $x^{2} + 2xysec\ \theta + y^{2} = 0$ is

Explanation

Reviewed by Dr. Abubacker

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