Question

A rectangle R with endpoints of the one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x – y + 4 = 0, then the area of R is ______.

विकल्प

• 15

• 16

• 17

• 18

Answer 1

A rectangle R with endpoints of the one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x – y + 4 = 0, then the area of R is 16.

Explanation:

Let the rectangle R with endpoints PQRS and P(1, 2) find Q(3, 6).

Slope of PQ = 2

Slope of given diameter = 2

Equation of line PQ is (y – 2) = 2(x – 1) ⇒ y = 2x.

So the diameter is parallel to PQ

Distance between diameter and line PQ. 

= `(4/sqrt(2^2 + 1^2))`

= `4/sqrt(5)`

Thus RQ = `2 xx 4/sqrt(5)` = `8/sqrt(5)`

Take PQ = `sqrt((1 - 3)^2 + (2 - 6)^2`

= `sqrt(20)`

= `2sqrt(5)`

Area = PQ × RQ

= `8/sqrt(5) + 2sqrt(5)`

= 16 sq.units.