The point (i,i+1) will lie inside circle x² + y2 - 2x + 4y = 0
A) For i=-1
B) For i = -2
C) For all i
D) For no i
E) For i = 1
Pls show solution
Answers
Answer:
A : -1
Step-by-step explanation:
as the centre is (1,-2)
and radius √5
if we put -1 as i it will be inside the circle...
Given:
The equation of a circle is x² + y² - 2x + 4y = 0 .
To Find:
The value of ( i ) such that the point (i,i+1) lies inside the given circle.
Solution:
The given problem can be solved by using the concepts of circles.
1. For a point (h,k) to lie inside the circle x² + y² + 2gx + 2fy +c = 0 . The value of h² + k² + 2h + 4k +c must be less than 0 . If the value is greater than 0 the point lies outside the circle and if the value is equal to 0 then the point lies on the circle.
2. Using the above property, the point (i,i+1) when substituted in the circle equation must have a value less than 0.
=> i² + (i+1)² - 2i + 4(i+1) < 0,
=> i² + i² + 2i + 1 - 2i + 4i +4 < 0 .
=> 2i² + 4i + 5 < 0 .
3. The value of the expression 2i² + 4i + 5 is always greater than 0 for all values of x. Hence, the above inequality has no values of i. Hence, for any values of ( i )the point (i,i+1) cannot lie in the given circle.
Therefore, Option C is the correct answer.