Question

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

• A. 16
• B. 32
• C. 8
• D. None of these

Answer 1

The correct option is B

32

AB = 8, M = (1, 4)

Let centre of circle is O(h, k)

$\because AB$ is parallel to X axis

$\Rightarrow MN$ is parallel to Y axis

$\Rightarrow h=1$

Now 4y = x + 7 is a diameter

4k = h + 7

4k = 1 + 7

k = 2

$\Rightarrow O(1,2)$

$\Rightarrow OM=2$

$\Rightarrow MN=4$

Area =$8\times 4=32$