mth101 ASSIGNMENT#1 Fall 2021 Solutions
ASSIGNMENT#1
Fall 2021 MTH101
I'd:
Course code : MTH101
Course name: calculus and Analytical geometry
Question
Marks=10
Consider the equation of a circle 
If the line 
is its diameter. Then find the value of a.
Solution:
x² + y² + 2gx + fy + c = 0
Center (-g,
-f) and radius=√g²+f²-c
Given circle equation
x² +
2x + y² - 4 = 0
This can be written as
x²
+ y² - 2x4y - 4= 0
Comparing general equation given equation of circle 2g =
-2
g = -2/2
g
= -1
2f = -2 Or
C = -4
So center (-g , -f) = (1 ,2)
Radius = 3
Because diameter pass through the center
so center point satisfiled the given diameter equation
Diameter equation
2x - y + a =0
2(1) - 2 + a = 0
2 - 2 + a = 0
a = 0
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