Table of contents  
The Standard Form of Circle  
The Ellipse  
The Parabola  
The Hyperbola 
Example 1: If the area of the circle shown below is kπ, what is the value of k?
(a) 4
(b) 16
(c) 32
(d) 20
Correct Answer is Option (c)
Since the line segment joining (4, 4) and (0, 0) is a radius of the circle:
r^{2} = 4^{2} + 4^{2} = 32
Therefore, area = πr^{2} = 32π ⇒ k = 32
Example 2: Find the area enclosed by the figure  x  +  y  = 4.
The four possible lines are:
x + y = 4; x  y = 4;  x  y = 4 and x + y = 4
The four lines can be represented on the coordinates axes as shown in the figure. Thus a square is formed with the vertices as shown. The side of the square is:
The area of the square is = 32 sq. units.
Example 3: If point (t, 1) lies inside circle x^{2} + y^{2 }= 10, then t must lie between:
As (t, 1) lies inside the circle, so its distance from centre i.e. origin should be less than radius i.e.
Example.4 Find the equation of line passing through (2, 4) and through the intersection of line 4x  3y  21 = 0 and 3x  y  12 = 0?
4x  3y  21 = 0 …..(1)
3x  y  12 = 0 ….(2)
Solving (1) and (2), we get point of intersection as x = 3 & y =  3.
Now we have two points (3, 3) & (2, 4)
⇒ Slope of line m = =  7
So, the equation of line is:
⇒ y + 3 =  7 (x  3)
⇒ 7x + y  18 = 0
Alternate Method:
Equation of line through intersection of 4x  3y  21 = 0 and 3x  y  12 = 0 is:
(4x  3y  21) + k(3x  y  12) = 0.
As this line passes through (2, 4):
⇒ (4 × 2  3 × 4  21) + k(3 × 2  4  12) = 0
⇒ k =
So, the equation of line is:
197 videos151 docs200 tests

1. What is the standard form of a circle? 
2. How is an ellipse different from a circle? 
3. What is the equation of a parabola? 
4. How can you distinguish between a hyperbola and an ellipse? 
5. How can the standard form of each conic section be used in reallife applications? 
197 videos151 docs200 tests


Explore Courses for UPSC exam
