Example 4 - Chapter 11 Class 11 Conic Sections
Last updated at Feb. 6, 2020 by Teachoo
Last updated at Feb. 6, 2020 by Teachoo
Transcript
Example 4 Find the equation of the circle which passes through the points (2, –2), and (3,4) and whose centre lies on the line x + y = 2. Equation of circle with centre (h, k) is (x – h)2 + (y – k)2 = r2 Since the circle passes through (2, – 2) Point (2, −2) will satisfy the equation of circle Putting x = 2, y = −2 in (A) (2 − h)2 + (−2 − k)2 = r2 4 + h2 − 4h + 4 + (−2)2 + (−k)2 + 2(−2)(−k) = r2 4 + h2 − 4h + 4 + k2 + 4k = r2 h2 + k2 − 4h + 4k + 8 = r2 Similarly , Since circle passes through (3, 4) Point (3, 4) will satisfy the equation of circle Putting x = 3, y = 4 in (A) (3 − h)2 + (4 − k)2 = r2 (3)2 + (h)2 − 2(3)(h) + (4)2 + (k)2 − 2(4)(k) = r2 9 + h2 − 6h + 16 + k2 − 8k = r2 h2 + k2 − 6h − 8k + 25 = r2 Subtracting (2) from (1) (h2 + k2 − 6h − 8k + 25) − (h2 + k2 − 4h + 4k + 8) = r2 − r2 h2 + k2 − 4h + 4k + 8 − h2 − k2 + 6h + 8k − 25 = 0 h2 − h2 + k2 − k2 − 4h + 6h + 4k + 8k + 8 − 25 = 0 0 + 0 + 2h + 12k − 17 = 0 2h + 12k – 17 = 0 Since center (h, k) lie on the line x + y = 2 i.e. point (h, k) will satisfy the equation of circle h + k = 2 Now our equations are 2h + 12k = 17 h + k = 2 From (4) h + k = 2 k = 2 − h Putting value of k in (3) 2h + 12(2 − h) = 17 2h + 24 − 12h = 17 −10h = 17 − 24 −10h = −7 h = (−7)/(−10) h = 0.7 Putting value of h = 0.7 in k = 2 − h k = 2 − (0.7) k = 1.3 Putting value of (h, k) = (0.7, 1.3) in (A) (x – h)2 + (y – k)2 = r2 (2 − 0.7)2 + (−2 − 1.3)2 = r2 (1.3)2 + (−3.3)2 = r2 1.69 + 10.89 = r2 12.58 = r2 r2 = 12.58 Putting value of h, k & r2 in (A) (x − 0.7)2 + (y − 1.3)2 = 12.58 Hence required equation circle is (x − 0.7)2 + (y − 1.3)2 = 12.58
Examples
Example 2
Example 3 Important
Example 4 Important You are here
Example 5
Example 6 Important
Example 7 Important
Example 8 Important
Example 9
Example 10 Important
Example, 11
Example 12 Important
Example 13 Important
Example 14 Important
Example 15
Example 16 Important
Example 17
Example 18 Important
Example, 19 Important
Examples
About the Author