16. If one end of the diameter of a circle with centre as
origin is (-2, 10), then the length of diameter of the
circle is
(1) 3/97 units
(2) 2186 units
(3) 183 units
(4) /416 units
Answers
Method 1.
When the centre of a circle along with one end of a diameter is given, to obtain the length of the diameter, we simply twice the radius formed by those points.
Step-by-step explanation:
The centre of the circle is at the origin O (0, 0) and one end of the diameter being (- 2, 10)
Then the radius of the circle is
= √{(0 + 2)² + (0 - 10)²} units
= √(2² + 10²) units
= √(4 + 100) units
= √104 units
= 2√26 units
Therefore the length of the diameter is
= 2 * 2√26 units
= 4√26 units
= √416 units
Method 2.
If any circle with centre (a, b) has end points of a diameter being (x₁, y₁) and (x₂, y₂), then a, b are obtained from
a = (x₁ + x₂)/2 , b = (y₁ + y₂)/2
Step-by-step explanation:
Given that the given circle has centre at the origin O (0, 0) and one end of a diameter being (- 2, 10).
If (x, y) be another end of that diameter, then from the above relations, we write
0 = (x - 2)/10 , 0 = (y + 10/2)
i.e., x = 2 , y = - 10
∴ the other end of the diameter is (2, - 10)
Hence the length of the diameter is
= √{(- 2 - 2)² + (10 + 10)²} units
= √(4² + 20²) units
= √(16 + 400) units
= √416 units
So, Option (4) is correct.