# MTH101 Assignment Solution # 1 Fall 2021

MTH101 Assignment Solution # 1 Fall 2021

**MTH101 Assignment Solution # 1 Fall 2021**

**Assignment No. 1Semester: Fall 2021**

**Question:**

**Consider the equation of a circle x ^{2}-2x+y^{2}-4y-4=0. If the line **

**2x- y+a=0 is its diameter. Then find the value of a.**

**Solution :**

x²-2x+y²-4y-4=0 …… (1)

General Form is

x²+y²+2gx+2fy+c=0 ……. (2)

Comparing eq 1 and 2

2g=-2 g=-1

2f=-4

f=-2

**We know that**

Center (-g, -f)

C (1, 2)

**Diameter lines pass** through the point of the circle of the **center of **

**circle, So the center point is satisfying the line.**

2x-y+a=0

2(1)-(2) +a=0

2-2+a=0

-2+a= -2

a = -2+2

**a=0**