1.

10.If the area of the circle x2+y2-4x-2y+k=0 is 250 sq. cms,then k=1)-202) 203) + 20 430​

Answer»

ANSWER :

k = -74.6

Solution :

★ Note : The standard form of a circle is given as : (x - H)² + (y - k)² = r² where (h,k) is the centre and r is the radius of the circle .

Here ,

The given equation of circle is ;

x² + y² - 4x - 2y + k = 0

The given equation of circle can be rewritten as ;

=> x² - 4x + y² - 2y = -k

=> (x² - 4x + 2²) + (y² - 2y + 1²) = 2² + 1² - k

=> (x - 2)² + (y - 1)² = 4 + 1 - k

=> (x - 2)² + (y - 1)² = 5 - k

Now ,

Comparing the above equation with the standard form (x - h)² + (y - k)² = r² , we have r² = 5 - k .

ALSO ,

The AREA of given circle is 250 cm² .

=> A = 250

=> π•r² = 250

=> π•(5 - k) = 250

=> 3.14•(5 - k) = 250

=> 5 - k = 250/3.14

=> 5 - k = 79.6

=> k = 5 - 79.6

=> k = -74.6

Hence k = -74.6


Discussion

No Comment Found

Related InterviewSolutions