Bissoy.com
Doctors Medicines MCQs Q&A

Find the equation of a circle with centre at (a cos α, a sin α) and radius is of 'a' units ?

Find the equation of a circle with centre at (a cos α, a sin α) and radius is of 'a' units ? Correct Answer x<span style="position: relative; line-height: 0; vertical-align: baseline; top: -0.5em;font-size:10.5px;">2</span> + y<span style="position: relative; line-height: 0; vertical-align: baseline; top: -0.5em;font-size:10.5px;">2</span> - 2ax cos α - 2ay sin α = 0 

CONCEPT:

Equation of circle with centre at (h, k) and radius 'r' units is given by:

(x - h)2 + (y - k)2 = r2

CALCULATION:

Here, we have to find the equation of a circle with centre at (a cos α, a sin α) and radius is 'a' units.

As we know that the equation of circle with centre at (h, k) and radius 'r' units is given by (x - h)2 + (y - k)2 = r2

Here, we have h = a cos α, k = a sin α and r = a

So, the equation of the required circle is:

(x - a cos α)2 + (y - a sin α)2 = a2

⇒ x2 + y2 - 2ax cos α - 2ay sin α = 0 

So, the required equation of circle is x2 + y2 - 2ax cos α - 2ay sin α = 0 

Hence, option C is the correct answer.

Related Questions

Evaluate the following:
$$\frac{{\cos 2\theta \cdot \cos 3\theta - \cos 2\theta \cdot \cos 7\theta + \cos \theta \cdot \cos 10\theta }}{{\sin 4\theta \cdot \sin 3\theta - \sin 2\theta \cdot \sin 5\theta + \sin 4\theta \cdot \sin 7\theta }}$$
Find the ∫∫x3 y3 sin⁡(x)sin⁡(y) dxdy. ]) b) (-x3 Cos(x) – 3x2 Sin(x) – 6xCos(x)-6Sin(x))(-y3 Cos(y) + 3]) c) (-x3 Cos(x) + 3x2 Sin(x) + 6xCos(x)-6Sin(x))(-y3 Cos(y) + 3y2 Sin(y) + 6yCos(y) – 6Sin(y)) d) (–x3 Cos(x) + 6xCos(x) – 6Sin(x))(-y3 Cos(y))
The value of the expression:sin21° + sin211° + sin221° + sin231° + sin241° + sin245° + sin249° + sin259° + sin269° + sin279° + sin289° is?
Which of the following statements is/are true? A: If a circle is formed from a wire, which was initially in the shape of a semi-circle, then ratio of radius of circle and that of semi-circle will be 7: 11. B: If in a semi-circle of radius ‘r’, another semi-circle of radius ‘4r/5’ is drawn, then area of the remaining part of larger semi-circle will be ‘3πr2/5’. C: In a circle of radius ‘r’, if ‘O’ is the center of circle and radii OA and OB are at the angle of 45°, then the length of major arc AB will be ‘7πr/8’.
What is the value of {[sin (x + y) – 2 sin x + sin (x – y)]/[cos (x – y) + cos (x + y) – 2 cos x]} × [(sin 10x – sin 8x)/(cos 10x + cos 8x)]?
What is the value of $$\frac{{32{{\cos }^6}x - 48{{\cos }^4}x + 18{{\cos }^2}x - 1}}{{4\sin x\,\cos x\,\sin \left( {60 - x} \right)\cos \left( {60 - x} \right)\sin \left( {60 + x} \right)\cos \left( {60 + x} \right)}}?$$
Which two classes use the Shape class correctly?
A. public class Circle implements Shape { private int radius; }B. public abstract class Circle extends Shape { private int radius; }C. public class Circle extends Shape { private int radius; public void draw(); }D. public abstract class Circle implements Shape { private int radius; public void draw(); }E. public class Circle extends Shape { private int radius; public void draw() { /* code here */ } }F. public abstract class Circle implements Shape { private int radius; public void draw() { /* code here */ } }
An operating system uses the Banker’s algorithm for deadlock avoidance when managing the allocation of three resource types X, Y, and Z to three processes P0, P1, and P2. The table given below presents the current system state. Here, the Allocation matrix shows the current number of resources of each type allocated to each process and the Max matrix shows the maximum number of resources of each type required by each process during its execution.   Allocation Max   X Y Z X Y Z P0 0 0 1 8 4 3 P1 3 2 0 6 2 0 P2 2 1 1 3 3 3   There are 3 units of type X, 2 units of type Y and 2 units of type Z still available. The system is currently in a safe state. Consider the following independent requests for additional resources in the current state: REQ1: P0 requests 0 units of X, 0 units of Y and 2 units of Z REQ2: P1 requests 2 units of X, 0 units of Y and 0 units of Z Which one of the following is TRUE?
Find the value of (cos x + cos y) (sin x – sin y) / (cos x – cos y) (sin x + sin y), where x = 90° and y = 0°.
“What is the different between height and radius of solid cylinder?” Which of the following option is sufficient alone to find the answer? A) A solid cylinder is made by melting a solid sphere. The radius of cylinder is 3 times the radius of a circle whose area is 154 sq.m. Height of cylinder is equal to the height of cone whose volume is 2772 cubic meters. B) Area of a rectangle whose longer side is ¾ times the radius of a solid cylinder, is 168 sq.m and, Volume of solid cylinder is 2772 cubic meters and its height is 18 m. C) A metallic cone of radius 15m and height 35m is melted into the solid cylinder of radius equal to the radius of a circle whose area is equal to the area of rectangle whose sides are in the ratio 4 : 3 respectively. D) The curved surface area of the solid cylinder is 3 time the surface area of a sphere of radius 7m and height of cylinder is equal to the height of a metallic cone whose curved surface area is 308 sq.m.