In the given figure, a parabola is drawn to pass through the vertices B, C and D of the square are ABCD .If the coordinates of A and C are (2,1) and (2,3), respectively, then focus of this parabola is

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Infinity Learn · Accepted Answer

AC is parallel to y axis, its mid point is (2$$,$$2) .  Thus, B≡(3$$,$$2) and D≡(1$$,$$2) .  Equation of parabola is (x$$−$$2)2=$$λ$$(y$$−$$3) .  It passes through (3$$,$$2), so λ$$=$$−$$1$$ .  Thus, equation of parabola reduces to (x$$−$$2)2=$$−$$(y$$−$$3) .  Hence, axis is (x$$−$$2)2$$ and latus rectum line is y−$$3=$$−$$1/4$$ .  For focus, x−$$2=0$$ and y−$$3=$$−$$1/4$$ .  Therefore, focus is $$(2$$,$$11/4) .

In the given figure, a parabola is drawn to pass through the vertices B, C and D of the square are ABCD .If the coordinates of A and C are (2,1) and (2,3), respectively, then focus of this parabola is

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