### Solution: Determine the equation of the circle

#### Problem Statement:

Determine the equation of the circle whose radius is 5, center on the line x = 2 and tangent to the line 3x – 4y + 11 = 0.

The equation of the circle is (x – 2)2 + (y + 2)2 = 25.

Solution:

### Solution: Find the area of the circle whose equation is x^2 + y^2 = 6x – 8y.

#### Problem Statement:

Find the area (in square units) of the circle whose equation is x^2 + y^2 = 6x – 8y.

The are of the circle given the equation is 25Ï€ sq. units.

Solution:

### Solution: Find the other end of the diameter through (-1, -3)

#### Problem Statement: EE Board April 1997

The center of a circle is at (1, 1) and one point on its circumference is (-1, -3). Find the other end of the diameter through (-1, -3).

The other end of the diameter is P(3, 5).

Solution:

### Solution: The equation x^2 + y^2 – 4x + 2y – 20 = 0 describes

#### Problem Statement: ME Board October 1996

The equation x^2 + y^2 – 4x + 2y – 20 = 0 describes:

The equation describes a a circle of radius 5 centered at (2, -1).

Solution:

### Solution: What is the shortest distance from A(3, 8) to the circle x^2 + y^2 + 4x – 6y = 12?

#### Problem Statement: CE Board November 1993

What is the shortest distance from A(3, 8) to the circle x^2 + y^2 + 4x – 6y = 12?

The shortest distance from A(3, 8) to the circle is 2.1 units.

Solution:

### Solution: What is the distance between the centers of the circles?

#### Problem Statement:

What is the distance between the centers of the circles x^2 + y^2 + 2x + 4y – 3 = 0 and x^2 + y^2 + 2x – 8x – 6y + 7 = 0?

The distance between the centers of the circles is equal to 7.07 units.

Solution:

### Solution: How far from the y-axis is the center of the curve 2x^2 + 2y^2 +10x – 6y – 55 = 0?

#### Problem Statement: CE Board May 1996

How far from the y-axis is the center of the curve 2x^2 + 2y^2 +10x – 6y – 55 = 0?

The distance of the center of the curve from the y-axis is equal to -2.5 unit (the negative sign denotes on the left of the y-axis).

Solution:

### Solution: What is the diameter of a circle described by 9x^2 + 9y^2 = 16?

#### Problem Statement: ECE Board April 1998

What is the diameter of a circle described by 9x^2 + 9y^2 = 16?

The diameter of the circle is 8/3.

Solution:

### Solution: What is the radius of a circle with the ff. equation: x^2 – 6x + y^2 – 4y – 12 = 0?

#### Problem Statement: ME Board April 1998

What is the radius of a circle with the following equation: x^2 – 6x + y^2 – 4y – 12 = 0?

The radius of the circle is 5

Solution:

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