One of the diameters of the circle circumscribing the rectangle ABCD is $$4y$$ $$=$$ x $$+$$ $$7$$. If A and Bare the points $$(-3$$,$$4)$$ and (5$$, $$4) respectively, then the area of the rectangle, in square units, is

Question

One of the diameters of the circle circumscribing the rectangle ABCD is $$4y$$ $$=$$ x $$+$$ $$7$$. If A and Bare the points $$(-3$$,$$4)$$ and (5$$, $$4) respectively, then the area of the rectangle, in square units, is

Infinity Learn · Accepted Answer

Let the equation of the circle $$bex2+y2+2gx+2fy+c=0This$$ passes through $$(-$$ $$3$$, $$4)$$ and (5$$, $$4).∴    −$$6g+8f+c+25=0$$ and, $$10g+8f+c+41=0Subtracting$$ (ii) from (i), we get g $$=$$ $$-1$$. Since the centre $$(-$$ g, $$-$$ $$f)$$ lies on $$4$$ y $$=$$ x $$+$$ $$7$$∴ −$$4f=$$−$$g+7$$⇒So, centre of the circle is at $$(1$$, $$2)Now$$, AD $$=$$ $$2$$ $$GM=$$> AD $$=$$ $$2$$ $$(Length$$ of the .l from G on AB whose eqn. is⇒ $$AD=2$$×$$2=4$$ Also, $$AB=8Hence$$, area of rectangle ABCD $$=c$$ $$4$$ x $$8$$ $$=$$ $$32$$ sq. units.

Definition of a circle

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One of the diameters of the circle circumscribing the rectangle $A B C D$ is $4 y = x + 7$ . If A and Bare the points (-3,4) and (5, 4) respectively, then the area of the rectangle, in square units, is

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Definition of a circle

Remember concepts with our Masterclasses.

One of the diameters of the circle circumscribing the rectangle ABCD is 4y = x + 7. If A and Bare the points (-3,4) and (5, 4) respectively, then the area of the rectangle, in square units, is

Ready to Test Your Skills?

free study material

One of the diameters of the circle circumscribing the rectangle $A B C D$ is $4 y = x + 7$ . If A and Bare the points (-3,4) and (5, 4) respectively, then the area of the rectangle, in square units, is