If the curve $$x2+2y2=2$$ intersects the line x $$+$$ y $$=$$ $$1$$ at two points P and Q, then the angle subtended by the line segment PQ is at the origin is

Question

If the curve $$x2+2y2=2$$ intersects the line x $$+$$ y $$=$$ $$1$$ at two points P and Q, then the angle subtended by the line segment PQ is at the origin is

Infinity Learn · Accepted Answer

Equation of the curve is $$x2+2y2=2$$⇒$$x22+y21=1$$            Equation of the line is  x  $$+$$ y $$=$$ $$1$$   ; y $$=$$ $$1-x$$            Solving the above two equations $$x2+21-x2=2x2+2x2+2$$−$$4x=23x2$$−$$4x=0x3x$$−$$4=0Hence$$ the values of x are $$0$$,$$43Hence$$, the points are  $$P(0$$,$$1)$$  ,$$Q43$$,−$$13The$$ line OP is vertical axis, the slope of OQ is $$-14hence$$ the angle subtended by OP and OQ at origin is   θ$$=$$  π$$2+$$$$tan$$$$-1(-14)$$   θ $$=$$ π$$2+$$$$tan$$$$-114$$

If the curve $x^{2} + 2 y^{2} = 2$ intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ is at the origin is

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If the curve x2+2y2=2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ is at the origin is

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If the curve $x^{2} + 2 y^{2} = 2$ intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ is at the origin is