The set of values of a for which the point (2a$$, $$a+1) is an interior point of the larger segment of the circle $$x2+y2-2x-2y-8=0made$$ by the chord $$x-y+1=0$$,is

Question

The set of values of a for which the point (2a$$, $$a+1) is an interior point of the larger segment of the circle $$x2+y2-2x-2y-8=0made$$ by the chord $$x-y+1=0$$,is

Infinity Learn · Accepted Answer

The point (2a$$, a $$+$$ $$1) will be an interior point of the larger segment of the circle $$x2+y2$$−$$2x$$−$$2y$$−$$8=0$$,if (i) the point (2a$$, a $$+$$ $$1) is an interior pointand, (ii) the point (2a$$, a $$+$$ $$1) and the centre (1$$, $$1) are on the sameside of the chord x $$-$$ y $$+$$ $$1$$ $$=$$ $$0$$.and, (2a$$−a−$$1+1)(1$$−$$1+1)>$$0$$⇒ $$5a2$$−$$4a$$−$$9$$<$$0$$ and a>$$0$$⇒ (5a$$−$$9)(a+1)<$$0$$ and a>$$0$$⇒ −$$10$$⇒a∈(0$$,$$9/5)

The set of values of a for which the point $(2 a, a + 1)$ is an interior point of the larger segment of the circle $x^{2} + y^{2} - 2 x - 2 y - 8 = 0$ made by the chord $x - y + 1 = 0,$ is

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The set of values of a for which the point (2a, a+1) is an interior point of the larger segment of the circle x2+y2-2x-2y-8=0made by the chord x-y+1=0,is

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The set of values of a for which the point $(2 a, a + 1)$ is an interior point of the larger segment of the circle $x^{2} + y^{2} - 2 x - 2 y - 8 = 0$ made by the chord $x - y + 1 = 0,$ is