# Ex 11.1, 13

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 11.1, 13 Find the equation of the circle passing through (0, 0) and making intercepts a and b on the coordinate axes. Let the equation of circle be (x – h)2 + (y – k)2 = r2 where (h, k) is the centre & r is the radius of a circle Also given that circle making intercepts a & b on the coordinate axes Let intercept on x-axis be a, So, coordinates of point A (a, 0) Let intercept on y-axis be b, So, coordinates of point B (0, b) Now, given that circle passes through (0, 0) So, Point (0, 0) will satisfy the equation of circle Putting x = 0 & y = 0 in (1) (0 − h)2 + (0 − k)2 = r2 h2 + k2 = r2 Also, point A (a, 0) lies on circle So, point A(a, 0) will satisfy the equation of circle Putting x = a & y = 0 in (1) (a − h)2 + (0 − k)2 = r2 (a − h)2 + k2 = r2 a2 + h2 − 2ah + k2 = r2 h2 + k2 + a2 − 2ah = r2 Putting h2 + k2 = r2 from (2) r2 + a2 − 2ah = r2 a2 − 2ah = r2 − r2 a(a − 2h) = 0 a − 2h = 0 h = 𝑎 2 Similarly, Point B(0, b) lie on the circle Point B(0, b) will satisfy the equation of circle Putting x = 0 & y = b in (1) (0 – h)2 + (b – k)2 = r2 h2 + (b – k)2 = r2 h2 + b2 + k2 − 2bk = r2 h2 + k2 + b2 − 2bk = r2 Putting h2 + k2 = r2 from (2) r2 + b2 − 2ah = r2 b2 − 2bk = r2 − r2 b(b − 2k) = 0 b − 2k = 0 b = 2k 2k = b k = 𝑏 2 Thus, h = 𝑎 2 & k = 𝑏 2 So, C(h, k) = 𝑎2, 𝑏2 Now we need to find radius of circle Putting h = 𝑎2 & b = 𝑏2 in (2) h2 + k2 = r2 𝑎22 + 𝑏22 = r2 𝑎24 + 𝑏24 = r2 𝑎2 + 𝑏24 = r2 r2 = 𝑎2 + 𝑏24 Putting value of (h, k) & r2 in (1) (x – h)2 + (y – k)2 = r2 𝑥− 𝑎22 + 𝑦−𝑏22 = 𝑎2 + 𝑏24 (x)2 + 𝑎22 − 2(x) 𝑎2 + y2 +𝑏22 − 2(y) 𝑏2 = 𝑎2 + 𝑏24 x2 + 𝑎24 − ax + y2 + 𝑏24 − by = 𝑎2 + 𝑏24 x2 + y2 − ax − by + 𝑎24 + 𝑏24 = 𝑎2 + 𝑏24 x2 + y2 − ax − by + 𝑎2 + 𝑏24 = 𝑎2 + 𝑏24 x2 + y2 − ax − by = 𝑎2 + 𝑏24 − 𝑎2 + 𝑏24 x2 + y2 − ax − by = 0 Which is required equation of circle

Chapter 11 Class 11 Conic Sections

Serial order wise

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CA Maninder Singh

CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .